[ { "id": "Financial_mathematics_0000", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "3", "keywords": [ "financial mathematics", "annuities" ], "problem_v1": "Suppose that an annuity produces one payment per year for 20 years, starting on July 4, 1776. If the nominal rate of interest is 9.3 percent convertible semiannually, and the present value of the annuity on July 4, 1775 is 4500 dollars, how much is the annual payment?\nAnnual Payment=[ANS] dollars.", "answer_v1": [ "511.223061163532" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose that an annuity produces one payment per year for 17 years, starting on July 4, 1776. If the nominal rate of interest is 10.8 percent convertible semiannually, and the present value of the annuity on July 4, 1775 is 3100 dollars, how much is the annual payment?\nAnnual Payment=[ANS] dollars.", "answer_v2": [ "412.906688352572" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose that an annuity produces one payment per year for 18 years, starting on July 4, 1776. If the nominal rate of interest is 9.4 percent convertible semiannually, and the present value of the annuity on July 4, 1775 is 3600 dollars, how much is the annual payment?\nAnnual Payment=[ANS] dollars.", "answer_v3": [ "428.330642689297" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0001", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "2", "keywords": [ "financial mathematics", "annuities" ], "problem_v1": "Juan purchases an annuity for 4510 dollars that will make 20 annual payments, the first to come in one year. If the effective rate of interest is 9.3 percent, how much is each annual payment?\nAnswer=[ANS] dollars.", "answer_v1": [ "504.660745205622" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Juan purchases an annuity for 3160 dollars that will make 17 annual payments, the first to come in one year. If the effective rate of interest is 10.8 percent, how much is each annual payment?\nAnswer=[ANS] dollars.", "answer_v2": [ "413.62950893289" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Juan purchases an annuity for 3630 dollars that will make 18 annual payments, the first to come in one year. If the effective rate of interest is 9.4 percent, how much is each annual payment?\nAnswer=[ANS] dollars.", "answer_v3": [ "425.709210174556" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0002", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "2", "keywords": [ "financial mathematics", "annuities" ], "problem_v1": "Suppose that an annuity will provide for 15 payments, one every three years, of 3300 dollars. If the first payment will come 15 years from now, and the effective rate of interest is 10.4 percent, what is the present value of the annuity?\nAnswer=[ANS] dollars.", "answer_v1": [ "2879.09117364199" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose that an annuity will provide for 12 payments, one every three years, of 2500 dollars. If the first payment will come 15 years from now, and the effective rate of interest is 11.8 percent, what is the present value of the annuity?\nAnswer=[ANS] dollars.", "answer_v2": [ "1619.90845306477" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose that an annuity will provide for 13 payments, one every three years, of 2800 dollars. If the first payment will come 15 years from now, and the effective rate of interest is 10.4 percent, what is the present value of the annuity?\nAnswer=[ANS] dollars.", "answer_v3": [ "2419.52153376548" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0003", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "5", "keywords": [ "financial mathematics", "annuities" ], "problem_v1": "On January 1, 1999, Biff purchases an annuity for 52600 dollars. The annuity makes annual payments of the form $X, 2X, X, 2X,\\ldots$ with the first payment coming on January 1, 2000, and the final payment coming on January 1, 2040. Assuming an effective rate of 7.8 percent, what is $X$?\nAnswer=[ANS] dollars.", "answer_v1": [ "2906.92349181352" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "On January 1, 1999, Biff purchases an annuity for 45800 dollars. The annuity makes annual payments of the form $X, 2X, X, 2X,\\ldots$ with the first payment coming on January 1, 2000, and the final payment coming on January 1, 2040. Assuming an effective rate of 8.8 percent, what is $X$?\nAnswer=[ANS] dollars.", "answer_v2": [ "2816.44488745317" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "On January 1, 1999, Biff purchases an annuity for 48100 dollars. The annuity makes annual payments of the form $X, 2X, X, 2X,\\ldots$ with the first payment coming on January 1, 2000, and the final payment coming on January 1, 2040. Assuming an effective rate of 7.9 percent, what is $X$?\nAnswer=[ANS] dollars.", "answer_v3": [ "2687.81109003203" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0004", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "2", "keywords": [ "financial mathematics", "annuities" ], "problem_v1": "An annuity will make a payment every two months, starting two months from now. If the yield rate is 6.5 percent effective and the annuity will make 42 payments of 1260 dollars each, what is the price of the annuity?\nAnswer=[ANS] dollars.", "answer_v1": [ "42572.1751306433" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "An annuity will make a payment every two months, starting two months from now. If the yield rate is 4.6 percent effective and the annuity will make 49 payments of 580 dollars each, what is the price of the annuity?\nAnswer=[ANS] dollars.", "answer_v2": [ "23696.2341197895" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "An annuity will make a payment every two months, starting two months from now. If the yield rate is 5.2 percent effective and the annuity will make 42 payments of 810 dollars each, what is the price of the annuity?\nAnswer=[ANS] dollars.", "answer_v3": [ "28518.0280431163" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0005", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "5", "keywords": [ "financial mathematics", "annuities" ], "problem_v1": "Suppose that your grandparents give you 28000 dollars today as a graduation gift, and you deposit this money into an account that will earn an effective interest rate of 8.2 percent. You plan to make annual withdrawals from the account for as long as you can, with the first withdrawal being one year from now. Each withdrawal will be 5625 dollars, except for the last one which will be a smaller amount. What will be the amount of this final smaller withdrawal?\nAnswer=[ANS] dollars.", "answer_v1": [ "3738.52435392411" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose that your grandparents give you 20000 dollars today as a graduation gift, and you deposit this money into an account that will earn an effective interest rate of 9 percent. You plan to make annual withdrawals from the account for as long as you can, with the first withdrawal being one year from now. Each withdrawal will be 5150 dollars, except for the last one which will be a smaller amount. What will be the amount of this final smaller withdrawal?\nAnswer=[ANS] dollars.", "answer_v2": [ "5101.21945649999" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose that your grandparents give you 23000 dollars today as a graduation gift, and you deposit this money into an account that will earn an effective interest rate of 8.2 percent. You plan to make annual withdrawals from the account for as long as you can, with the first withdrawal being one year from now. Each withdrawal will be 5275 dollars, except for the last one which will be a smaller amount. What will be the amount of this final smaller withdrawal?\nAnswer=[ANS] dollars.", "answer_v3": [ "3287.8165789599" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0006", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "5", "keywords": [ "financial mathematics", "annuities" ], "problem_v1": "Puff Daddy wants to be sure that his lavish spending habits do not leave him bankrupt, so he will purchase an annuity. The annuity will make 27 semiannual payments of the form $8500,17000,8500,17000,\\ldots$, with the first payment coming 6 months after he purchases the annuity. If the annuity pays an interest rate of 7.8 percent convertible semiannually, how much should Puff Daddy pay for this annuity?\nAnswer=[ANS] dollars.", "answer_v1": [ "207730.894339479" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Puff Daddy wants to be sure that his lavish spending habits do not leave him bankrupt, so he will purchase an annuity. The annuity will make 21 semiannual payments of the form $6000,12000,6000,12000,\\ldots$, with the first payment coming 6 months after he purchases the annuity. If the annuity pays an interest rate of 8.8 percent convertible semiannually, how much should Puff Daddy pay for this annuity?\nAnswer=[ANS] dollars.", "answer_v2": [ "119674.200759381" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Puff Daddy wants to be sure that his lavish spending habits do not leave him bankrupt, so he will purchase an annuity. The annuity will make 23 semiannual payments of the form $7000,14000,7000,14000,\\ldots$, with the first payment coming 6 months after he purchases the annuity. If the annuity pays an interest rate of 7.8 percent convertible semiannually, how much should Puff Daddy pay for this annuity?\nAnswer=[ANS] dollars.", "answer_v3": [ "155124.355989262" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0007", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "5", "keywords": [ "financial mathematics", "perpetuities" ], "problem_v1": "Grandpa Joe decides to purchase a trust fund for his grandson Danny. The fund will start making payments 6 months from now, and will make semiannual payments forever. Grandpa Joe would like the payments to be of the form $X, 2X, X, 2X, X, 2X,\\ldots$, but it would cost him 11300 dollars for such a fund. Since he doesn't want to spend that much money, he instead decides to purchase a trust fund where the first 26 payments will be for 40 dollars each, and then the remaining payments will be of the form $X, 2X, X, 2X, X, 2X,\\ldots$. If the interest rate is 8.2 percent convertible semiannually, what is the price that Grandpa Joe pays for this trust fund?\nAnswer=[ANS] dollars.", "answer_v1": [ "4607.60644963485" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Grandpa Joe decides to purchase a trust fund for his grandson Danny. The fund will start making payments 6 months from now, and will make semiannual payments forever. Grandpa Joe would like the payments to be of the form $X, 2X, X, 2X, X, 2X,\\ldots$, but it would cost him 9200 dollars for such a fund. Since he doesn't want to spend that much money, he instead decides to purchase a trust fund where the first 30 payments will be for 25 dollars each, and then the remaining payments will be of the form $X, 2X, X, 2X, X, 2X,\\ldots$. If the interest rate is 7 percent convertible semiannually, what is the price that Grandpa Joe pays for this trust fund?\nAnswer=[ANS] dollars.", "answer_v2": [ "3737.56251282525" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Grandpa Joe decides to purchase a trust fund for his grandson Danny. The fund will start making payments 6 months from now, and will make semiannual payments forever. Grandpa Joe would like the payments to be of the form $X, 2X, X, 2X, X, 2X,\\ldots$, but it would cost him 9900 dollars for such a fund. Since he doesn't want to spend that much money, he instead decides to purchase a trust fund where the first 26 payments will be for 25 dollars each, and then the remaining payments will be of the form $X, 2X, X, 2X, X, 2X,\\ldots$. If the interest rate is 7.6 percent convertible semiannually, what is the price that Grandpa Joe pays for this trust fund?\nAnswer=[ANS] dollars.", "answer_v3": [ "4162.50492615295" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0008", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "3", "keywords": [ "algebra" ], "problem_v1": "\\$1760 is used to purchase an annuity consisting of equal payments at the end of each quarter for the next $6$ years. The interest rate is $6\\%$ compounded quarterly. Find the amount of each payment. \\$ [ANS]", "answer_v1": [ "87.8664194663358" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "\\$1080 is used to purchase an annuity consisting of equal payments at the end of each quarter for the next $3$ years. The interest rate is $9\\%$ compounded quarterly. Find the amount of each payment. \\$ [ANS]", "answer_v2": [ "103.698793670691" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "\\$1310 is used to purchase an annuity consisting of equal payments at the end of each quarter for the next $4$ years. The interest rate is $6\\%$ compounded quarterly. Find the amount of each payment. \\$ [ANS]", "answer_v3": [ "92.702251956907" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0009", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "2", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "Sally has a sum of \\$27000 that she invests at 10\\% compounded monthly. What equal monthly payments can she receive over a period of a) 8 years? Answer=\\$ [ANS]\nb) 15 years? Answer=\\$ [ANS]", "answer_v1": [ "409.702430640718", "290.143381781192" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Sally has a sum of \\$16000 that she invests at 7\\% compounded monthly. What equal monthly payments can she receive over a period of a) 10 years? Answer=\\$ [ANS]\nb) 8 years? Answer=\\$ [ANS]", "answer_v2": [ "185.773566749798", "218.13947328805" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Sally has a sum of \\$20000 that she invests at 8\\% compounded monthly. What equal monthly payments can she receive over a period of a) 8 years? Answer=\\$ [ANS]\nb) 10 years? Answer=\\$ [ANS]", "answer_v3": [ "282.733585090898", "242.655188710716" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0010", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "2", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "Find the amount of the annuity if the deposit is \\$1700 quarterly for 5 years at 11\\% compounded quarterly. Amount=\\$ [ANS]", "answer_v1": [ "44535.5757522223" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Find the amount of the annuity if the deposit is \\$600 quarterly for 7 years at 4\\% compounded quarterly. Amount=\\$ [ANS]", "answer_v2": [ "19277.4580138951" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Find the amount of the annuity if the deposit is \\$1000 quarterly for 5 years at 6\\% compounded quarterly. Amount=\\$ [ANS]", "answer_v3": [ "23123.6671033369" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0011", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "2", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "How many years will it take to exhaust an IRA of \\$230000 if you withdraw \\$2100 every month? Assume a rate of interest of 9\\% compounded monthly. Answer=[ANS] years", "answer_v1": [ "19.2135436350457" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "How many years will it take to exhaust an IRA of \\$150000 if you withdraw \\$2500 every month? Assume a rate of interest of 6\\% compounded monthly. Answer=[ANS] years", "answer_v2": [ "5.95943150129345" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "How many years will it take to exhaust an IRA of \\$180000 if you withdraw \\$2100 every month? Assume a rate of interest of 7\\% compounded monthly. Answer=[ANS] years", "answer_v3": [ "9.93095571466765" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0012", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "5", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "The Grand Prize in a State Lottery is \\$800000, which will be paid in 20 equal annual payments of \\$40000 each. The State makes the first payment right away. How much does the State need to deposit in an account paying 9\\% compounded annually to be able to make the remaining 19 equal annual payments of \\$40000 each? Answer=\\$ [ANS]", "answer_v1": [ "358004.591172146" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "The Grand Prize in a State Lottery is \\$500000, which will be paid in 25 equal annual payments of \\$20000 each. The State makes the first payment right away. How much does the State need to deposit in an account paying 6\\% compounded annually to be able to make the remaining 24 equal annual payments of \\$20000 each? Answer=\\$ [ANS]", "answer_v2": [ "251007.15055529" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "The Grand Prize in a State Lottery is \\$600000, which will be paid in 20 equal annual payments of \\$30000 each. The State makes the first payment right away. How much does the State need to deposit in an account paying 7\\% compounded annually to be able to make the remaining 19 equal annual payments of \\$30000 each? Answer=\\$ [ANS]", "answer_v3": [ "310067.857281069" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0013", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "2", "keywords": [ "percent" ], "problem_v1": "How many half-years will it take to exhaust a savings account of \\$230000 if you withdraw \\$26500 every half-year? Assume a nominal annual rate of interest of 7\\% compounded semi-annually. Answer=[ANS] half-years (answer to the nearest half-year.)", "answer_v1": [ "11" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "How many months will it take to exhaust a savings account of \\$150000 if you withdraw \\$30500 every month? Assume a nominal annual rate of interest of 4\\% compounded monthly. Answer=[ANS] months (answer to the nearest month.)", "answer_v2": [ "5" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "How many quarters will it take to exhaust a savings account of \\$180000 if you withdraw \\$26500 every quarter? Assume a nominal annual rate of interest of 5\\% compounded quarterly. Answer=[ANS] quarters (answer to the nearest quarter.)", "answer_v3": [ "7" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0014", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "4", "keywords": [ "percent" ], "problem_v1": "Mr. Brown wants to give his son an annuity of \\$ 5,000 per year starting on his twenty-first birthday, which will be increased to \\$ 10,000 per year on his twenty-fifth birthday, with the final payment on his thirtieth birthday. What is the present value of that annuity on his son's tenth birthday if the effective annual rate of interest is 12 \\%?\nPresent value on tenth birthday=\\$ [ANS]?", "answer_v1": [ "13302.48" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Mr. Brown wants to give his son an annuity of \\$ 5,000 per year starting on his twenty-first birthday, which will be increased to \\$ 10,000 per year on his twenty-fifth birthday, with the final payment on his thirtieth birthday. What is the present value of that annuity on his son's tenth birthday if the effective annual rate of interest is 3 \\%?\nPresent value on tenth birthday=\\$ [ANS]?", "answer_v2": [ "49643.37" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Mr. Brown wants to give his son an annuity of \\$ 5,000 per year starting on his twenty-first birthday, which will be increased to \\$ 10,000 per year on his twenty-fifth birthday, with the final payment on his thirtieth birthday. What is the present value of that annuity on his son's tenth birthday if the effective annual rate of interest is 6 \\%?\nPresent value on tenth birthday=\\$ [ANS]?", "answer_v3": [ "31423.86" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0015", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "1", "keywords": [ "arithmetic progression", "unknown interest rate" ], "problem_v1": "You are given the following that ${(Ia)}_{22\\rceil}$=62.36691. Calculate i. i=[ANS] \\%?", "answer_v1": [ "11" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "You are given the following that ${(Ia)}_{29\\rceil}$=248.60197. Calculate i. i=[ANS] \\%?", "answer_v2": [ "3" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "You are given the following that ${(Ia)}_{22\\rceil}$=110.98271. Calculate i. i=[ANS] \\%?", "answer_v3": [ "6" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0016", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "4", "keywords": [ "present value" ], "problem_v1": "An annuity provides for 35 annual payments. The first payment of \\$ 100 is made immediately and the remaining payments increase by 14 \\% per year. Interest is calculated at 19 \\% per year. Calculate the present value of the annuity.\nPresent value of annuity=\\$ [ANS]?", "answer_v1": [ "1850.21" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "An annuity provides for 20 annual payments. The first payment of \\$ 100 is made immediately and the remaining payments increase by 4 \\% per year. Interest is calculated at 20 \\% per year. Calculate the present value of the annuity.\nPresent value of annuity=\\$ [ANS]?", "answer_v2": [ "707.13" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "An annuity provides for 25 annual payments. The first payment of \\$ 100 is made immediately and the remaining payments increase by 7 \\% per year. Interest is calculated at 16 \\% per year. Calculate the present value of the annuity.\nPresent value of annuity=\\$ [ANS]?", "answer_v3": [ "1117.75" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0017", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "1", "keywords": [], "problem_v1": "For interest rate $i$, you are given $\\ddot a_{n\\rceil}$=8.51 and $\\ddot a_{2n\\rceil}$=14.08. Find $i$.\n$i$=[ANS] \\%", "answer_v1": [ "4.06" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "For interest rate $i$, you are given $\\ddot a_{n\\rceil}$=7.16 and $\\ddot a_{2n\\rceil}$=14.02. Find $i$.\n$i$=[ANS] \\%", "answer_v2": [ "0.59" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "For interest rate $i$, you are given $\\ddot a_{n\\rceil}$=7.63 and $\\ddot a_{2n\\rceil}$=13.18. Find $i$.\n$i$=[ANS] \\%", "answer_v3": [ "3.57" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0018", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "2", "keywords": [ "present value", "annuity immediate", "interest rate" ], "problem_v1": "Janet receives a \\$ 10,000 life insurance benefit. If she uses the proceeds to buy an n-year annuity immediate, the annual payout will be 1404.57. If a 2n-year annuity due is purchased, the annual payout will be 1226.01. Both calculations are based on an effective annual interest rate of i. Calculate i.\nEffective annual interest rate, i=[ANS] \\%?", "answer_v1": [ "12" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Janet receives a \\$ 10,000 life insurance benefit. If she uses the proceeds to buy an n-year annuity immediate, the annual payout will be 590.47. If a 2n-year annuity due is purchased, the annual payout will be 395.78. Both calculations are based on an effective annual interest rate of i. Calculate i.\nEffective annual interest rate, i=[ANS] \\%?", "answer_v2": [ "3" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Janet receives a \\$ 10,000 life insurance benefit. If she uses the proceeds to buy an n-year annuity immediate, the annual payout will be 954.45. If a 2n-year annuity due is purchased, the annual payout will be 695.98. Both calculations are based on an effective annual interest rate of i. Calculate i.\nEffective annual interest rate, i=[ANS] \\%?", "answer_v3": [ "6" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0019", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "5", "keywords": [ "arithmetic progression", "decreasing payments" ], "problem_v1": "Two annuities have the same present value. The first annuity is a decreasing annual annuity. The first payment is \\$ 2560, due one year from today. Subsequent annual payments decrease by \\$ 160 per year. The interest rate is 14 \\% compounded annually. The second annuity provides payments of \\$ K per month for 16 years. The first payment is due one month from today. What is K?\nValue of K=\\$ [ANS]?", "answer_v1": [ "139.26" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Two annuities have the same present value. The first annuity is a decreasing annual annuity. The first payment is \\$ 2200, due one year from today. Subsequent annual payments decrease by \\$ 110 per year. The interest rate is 4 \\% compounded annually. The second annuity provides payments of \\$ K per month for 20 years. The first payment is due one month from today. What is K?\nValue of K=\\$ [ANS]?", "answer_v2": [ "106.15" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Two annuities have the same present value. The first annuity is a decreasing annual annuity. The first payment is \\$ 2080, due one year from today. Subsequent annual payments decrease by \\$ 130 per year. The interest rate is 7 \\% compounded annually. The second annuity provides payments of \\$ K per month for 16 years. The first payment is due one month from today. What is K?\nValue of K=\\$ [ANS]?", "answer_v3": [ "104.06" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0020", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "1", "keywords": [ "arithmetic progression", "decreasing payments" ], "problem_v1": "Given that $i^{(10)}$=0.1, calculate ${(Da)}_{50\\rceil}$ at the annual effective rate. ${(Da)}_{50\\rceil}$=[ANS]", "answer_v1": [ "387.18" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Given that $i^{(2)}$=0.15, calculate ${(Da)}_{25\\rceil}$ at the annual effective rate. ${(Da)}_{25\\rceil}$=[ANS]", "answer_v2": [ "120.46" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Given that $i^{(5)}$=0.1, calculate ${(Da)}_{35\\rceil}$ at the annual effective rate. ${(Da)}_{35\\rceil}$=[ANS]", "answer_v3": [ "246.85" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0021", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "3", "keywords": [ "financial mathematics", "interest", "present value" ], "problem_v1": "If you want to be paid from a $14$ year ordinary annuity with a guaranteed rate of $5.725 \\%$ compounded annually, how much should you pay for one of these annuities if you want to receive annual payments of $\\\\$6{,}000.00$ over the $14$ year period? $[ANS]\n", "answer_v1": [ "56731.95" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "If you want to be paid from a $12$ year ordinary annuity with a guaranteed rate of $2.897 \\%$ compounded annually, how much should you pay for one of these annuities if you want to receive annual payments of $\\\\$10{,}000.00$ over the $12$ year period? $[ANS]\n", "answer_v2": [ "100154.85" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "If you want to be paid from a $13$ year ordinary annuity with a guaranteed rate of $3.671 \\%$ compounded annually, how much should you pay for one of these annuities if you want to receive annual payments of $\\\\$7{,}000.00$ over the $13$ year period? $[ANS]\n", "answer_v3": [ "71348.44" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0022", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Income streams", "level": "3", "keywords": [ "financial mathematics", "interest", "future value" ], "problem_v1": "If $\\\\$475.00$ is deposited at the end of each year for 6 years into an ordinary annuity earning $6.39 \\%$ interest compounded semiannually, construct a balance sheet showing the interest earned during each year and the balance at the end of each year. Assume this annuity rounds the interest and balance to the nearest penny at the end of each year.\n$\\begin{array}{cccc}\\hline Year & Payment & Interest & Balance \\\\\\hline1 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline2 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline3 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline4 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline5 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline6 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline\\end{array}$\n", "answer_v1": [ "475.00", "0.00", "475.00", "475.00", "30.84", "980.84", "475.00", "63.68", "1519.52", "475.00", "98.65", "2093.17", "475.00", "135.89", "2704.06", "475.00", "175.55", "3354.61" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [] ], "problem_v2": "If $\\\\$580.00$ is deposited at the end of each year for 6 years into an ordinary annuity earning $3.37 \\%$ interest compounded semiannually, construct a balance sheet showing the interest earned during each year and the balance at the end of each year. Assume this annuity rounds the interest and balance to the nearest penny at the end of each year.\n$\\begin{array}{cccc}\\hline Year & Payment & Interest & Balance \\\\\\hline1 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline2 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline3 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline4 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline5 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline6 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline\\end{array}$\n", "answer_v2": [ "580.00", "0.00", "580.00", "580.00", "19.71", "1179.71", "580.00", "40.09", "1799.80", "580.00", "61.16", "2440.96", "580.00", "82.95", "3103.91", "580.00", "105.48", "3789.39" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [] ], "problem_v3": "If $\\\\$482.00$ is deposited at the end of each year for 6 years into an ordinary annuity earning $4.41 \\%$ interest compounded semiannually, construct a balance sheet showing the interest earned during each year and the balance at the end of each year. Assume this annuity rounds the interest and balance to the nearest penny at the end of each year.\n$\\begin{array}{cccc}\\hline Year & Payment & Interest & Balance \\\\\\hline1 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline2 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline3 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline4 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline5 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline6 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline\\end{array}$\n", "answer_v3": [ "482.00", "0.00", "482.00", "482.00", "21.49", "985.49", "482.00", "43.94", "1511.43", "482.00", "67.39", "2060.82", "482.00", "91.88", "2634.70", "482.00", "117.47", "3234.17" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [] ] }, { "id": "Financial_mathematics_0023", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "simple", "interest" ], "problem_v1": "Mary purchases a new air conditioner for 5580 dollars, and takes out an add-on interest loan at 10.3 percent. If she is to pay off the loan in 36 monthly installments, how much is her monthly payment? Answer=[ANS] dollars.", "answer_v1": [ "202.895" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Mary purchases a new air conditioner for 5940 dollars, and takes out an add-on interest loan at 8.2 percent. If she is to pay off the loan in 24 monthly installments, how much is her monthly payment? Answer=[ANS] dollars.", "answer_v2": [ "288.09" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Mary purchases a new air conditioner for 5600 dollars, and takes out an add-on interest loan at 8.9 percent. If she is to pay off the loan in 24 monthly installments, how much is her monthly payment? Answer=[ANS] dollars.", "answer_v3": [ "274.866666666667" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0024", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "5", "keywords": [ "financial mathematics", "varying payments" ], "problem_v1": "To buy a condo, Sally takes out a 15-year mortgage of 130000 dollars at a nominal interest rate of 6.6 percent convertible monthly, with the first payment due in one month. If she will make monthly payments that increase by 0.03 percent per month, how much is her first payment? Answer=[ANS] dollars.", "answer_v1": [ "1114.14292598504" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "To buy a condo, Sally takes out a 15-year mortgage of 100000 dollars at a nominal interest rate of 5.1 percent convertible monthly, with the first payment due in one month. If she will make monthly payments that increase by 0.04 percent per month, how much is her first payment? Answer=[ANS] dollars.", "answer_v2": [ "771.354001593251" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "To buy a condo, Sally takes out a 15-year mortgage of 110000 dollars at a nominal interest rate of 5.7 percent convertible monthly, with the first payment due in one month. If she will make monthly payments that increase by 0.03 percent per month, how much is her first payment? Answer=[ANS] dollars.", "answer_v3": [ "889.653468516644" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0025", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "5", "keywords": [ "financial mathematics", "varying payments" ], "problem_v1": "Suppose you take out a 7-year loan at an interest rate of 8.7 percent convertible monthly. You will make monthly payments, with your first payment coming in one month. Your first payment will be for 1200 dollars, and your payments will increase by 18 dollars per month. How much interest is in the 11th payment? Answer=[ANS] dollars.", "answer_v1": [ "819.022879899207" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose you take out a 5-year loan at an interest rate of 6 percent convertible monthly. You will make monthly payments, with your first payment coming in one month. Your first payment will be for 1450 dollars, and your payments will increase by 8 dollars per month. How much interest is in the 15th payment? Answer=[ANS] dollars.", "answer_v2": [ "355.688573520757" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose you take out a 6-year loan at an interest rate of 6.9 percent convertible monthly. You will make monthly payments, with your first payment coming in one month. Your first payment will be for 1250 dollars, and your payments will increase by 10 dollars per month. How much interest is in the 11th payment? Answer=[ANS] dollars.", "answer_v3": [ "489.632068337344" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0026", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "5", "keywords": [ "financial mathematics", "varying payments" ], "problem_v1": "Jill borrows 17020 dollars from a line of credit at a rate of 8.1 percent convertible monthly. At the end of each month, in addition to the interest charged on the account balance, there is a fee charged to the account. The fee is 55 dollars at the end of the first month, and will increase by 2.1 percent each month that follows. How much does Jill owe after 12 months have passed, assuming she makes no payments? (Note: Assume that she has just been charged the interest and fee for the 12th month.)\nAnswer=[ANS] dollars.", "answer_v1": [ "19219.685954905" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Jill borrows 14320 dollars from a line of credit at a rate of 6.9 percent convertible monthly. At the end of each month, in addition to the interest charged on the account balance, there is a fee charged to the account. The fee is 65 dollars at the end of the first month, and will increase by 1.9 percent each month that follows. How much does Jill owe after 14 months have passed, assuming she makes no payments? (Note: Assume that she has just been charged the interest and fee for the 14th month.)\nAnswer=[ANS] dollars.", "answer_v2": [ "16585.8153672777" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Jill borrows 15260 dollars from a line of credit at a rate of 7.2 percent convertible monthly. At the end of each month, in addition to the interest charged on the account balance, there is a fee charged to the account. The fee is 55 dollars at the end of the first month, and will increase by 2 percent each month that follows. How much does Jill owe after 11 months have passed, assuming she makes no payments? (Note: Assume that she has just been charged the interest and fee for the 11th month.)\nAnswer=[ANS] dollars.", "answer_v3": [ "16986.8326079865" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0027", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "5", "keywords": [ "financial mathematics", "varying payments" ], "problem_v1": "Jeremy takes out a loan at an effective interest rate of 7.75 percent. He will make 27 annual payments, with the first payment due in one year. The first payment will be 2400 dollars, and each payment that follows will be 0.55 percent more than the previous payment. How much does he owe on the loan immediately after the 15th payment? Answer=[ANS] dollars.", "answer_v1": [ "20408.8513859224" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Jeremy takes out a loan at an effective interest rate of 6.25 percent. He will make 23 annual payments, with the first payment due in one year. The first payment will be 2000 dollars, and each payment that follows will be 0.75 percent more than the previous payment. How much does he owe on the loan immediately after the 15th payment? Answer=[ANS] dollars.", "answer_v2": [ "14089.2913628373" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Jeremy takes out a loan at an effective interest rate of 6.75 percent. He will make 25 annual payments, with the first payment due in one year. The first payment will be 2100 dollars, and each payment that follows will be 0.55 percent more than the previous payment. How much does he owe on the loan immediately after the 15th payment? Answer=[ANS] dollars.", "answer_v3": [ "16559.2601625087" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0028", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "financial mathematics", "loans" ], "problem_v1": "Deborah borrows 5500 dollars from the bank at an effective rate of interest of 6.2 percent. The loan is to be repaid with 12 equal annual payments, the first coming a year from now. How large is each payment?\nAnswer=[ANS] dollars.", "answer_v1": [ "663.235758350158" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Deborah borrows 4100 dollars from the bank at an effective rate of interest of 6.9 percent. The loan is to be repaid with 9 equal annual payments, the first coming a year from now. How large is each payment?\nAnswer=[ANS] dollars.", "answer_v2": [ "626.62017926924" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Deborah borrows 4600 dollars from the bank at an effective rate of interest of 6.2 percent. The loan is to be repaid with 10 equal annual payments, the first coming a year from now. How large is each payment?\nAnswer=[ANS] dollars.", "answer_v3": [ "630.928141116769" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0029", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "financial mathematics", "loans" ], "problem_v1": "Jeff takes out a 32-year mortgage of 165000 dollars to purchase a home. Assume the rate of interest is 7.2 percent convertible monthly, and the first payment is due one month from now. If all the payments will be equal, how much is each monthly payment?\nAnswer=[ANS] dollars.", "answer_v1": [ "1100.67074315165" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Jeff takes out a 21-year mortgage of 195000 dollars to purchase a home. Assume the rate of interest is 6.3 percent convertible monthly, and the first payment is due one month from now. If all the payments will be equal, how much is each monthly payment?\nAnswer=[ANS] dollars.", "answer_v2": [ "1397.15013398488" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Jeff takes out a 25-year mortgage of 165000 dollars to purchase a home. Assume the rate of interest is 6.3 percent convertible monthly, and the first payment is due one month from now. If all the payments will be equal, how much is each monthly payment?\nAnswer=[ANS] dollars.", "answer_v3": [ "1093.55969729163" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0030", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "financial mathematics", "loans" ], "problem_v1": "Violet is planning to make 28 semiannual loan payments of 1640 dollars each. If her bank charges interest at a rate of 4.2 percent per half-year, how much principal is in the 22nd payment? Answer=[ANS] dollars.", "answer_v1": [ "1229.61687671474" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Violet is planning to make 25 semiannual loan payments of 1400 dollars each. If her bank charges interest at a rate of 4.9 percent per half-year, how much principal is in the 22nd payment? Answer=[ANS] dollars.", "answer_v2": [ "1156.1816781887" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Violet is planning to make 25 semiannual loan payments of 1540 dollars each. If her bank charges interest at a rate of 4.2 percent per half-year, how much principal is in the 22nd payment? Answer=[ANS] dollars.", "answer_v3": [ "1306.32080898975" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0031", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "5", "keywords": [ "financial mathematics", "loans" ], "problem_v1": "A loan of 15800 dollars is to be repaid in annual installments of 2200 dollars, the first due in one year, followed by a final smaller payment. If the effective rate of interest is 9.8 percent, what is the outstanding balance owed immediately after the 5th payment? Answer=[ANS] dollars.", "answer_v1": [ "11837.7258309547" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A loan of 12800 dollars is to be repaid in annual installments of 2300 dollars, the first due in one year, followed by a final smaller payment. If the effective rate of interest is 8.2 percent, what is the outstanding balance owed immediately after the 5th payment? Answer=[ANS] dollars.", "answer_v2": [ "5435.09141795912" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A loan of 13600 dollars is to be repaid in annual installments of 2200 dollars, the first due in one year, followed by a final smaller payment. If the effective rate of interest is 8.8 percent, what is the outstanding balance owed immediately after the 5th payment? Answer=[ANS] dollars.", "answer_v3": [ "7620.01776700948" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0032", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "5", "keywords": [ "financial mathematics", "loans" ], "problem_v1": "Dave takes out a 28-year mortgage of 260000 dollars for his new house. Dave gets an interest rate of 14.4 percent convertible monthly. He agrees to make equal monthly payments, the first coming in one month. After making the 68th payment, Dave wants to buy a boat, so he wants to refinance his house to reduce his monthly payment by 600 dollars, and to get a better interest rate. In particular, he negotiates a new rate of 8.4 percent convertible monthly, and agrees to make equal monthly payments (each 600 dollars less than his original payments) for as long as necessary, followed by a single smaller payment. How large will Dave's final loan payment be?\nAnswer=[ANS] dollars.", "answer_v1": [ "1963.47122427871" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Dave takes out a 20-year mortgage of 300000 dollars for his new house. Dave gets an interest rate of 14.4 percent convertible monthly. He agrees to make equal monthly payments, the first coming in one month. After making the 65th payment, Dave wants to buy a boat, so he wants to refinance his house to reduce his monthly payment by 500 dollars, and to get a better interest rate. In particular, he negotiates a new rate of 7.2 percent convertible monthly, and agrees to make equal monthly payments (each 500 dollars less than his original payments) for as long as necessary, followed by a single smaller payment. How large will Dave's final loan payment be?\nAnswer=[ANS] dollars.", "answer_v2": [ "715.426915449985" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Dave takes out a 23-year mortgage of 260000 dollars for his new house. Dave gets an interest rate of 14.4 percent convertible monthly. He agrees to make equal monthly payments, the first coming in one month. After making the 65th payment, Dave wants to buy a boat, so he wants to refinance his house to reduce his monthly payment by 600 dollars, and to get a better interest rate. In particular, he negotiates a new rate of 8.4 percent convertible monthly, and agrees to make equal monthly payments (each 600 dollars less than his original payments) for as long as necessary, followed by a single smaller payment. How large will Dave's final loan payment be?\nAnswer=[ANS] dollars.", "answer_v3": [ "2270.87518519993" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0033", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "5", "keywords": [ "financial mathematics", "loans" ], "problem_v1": "Ralph has just borrowed 1580 dollars to purchase a new stereo, at a nominal rate of interest of 11.8 percent convertible monthly. Although he is charged interest from the moment he borrows the money, the first payment is not due for 9 months. If he will make 24 monthly payments, how much interest is in the 17th payment? Answer=[ANS] dollars.", "answer_v1": [ "6.04428788831785" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Ralph has just borrowed 1280 dollars to purchase a new stereo, at a nominal rate of interest of 10.2 percent convertible monthly. Although he is charged interest from the moment he borrows the money, the first payment is not due for 11 months. If he will make 24 monthly payments, how much interest is in the 17th payment? Answer=[ANS] dollars.", "answer_v2": [ "4.21706595304349" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Ralph has just borrowed 1360 dollars to purchase a new stereo, at a nominal rate of interest of 10.8 percent convertible monthly. Although he is charged interest from the moment he borrows the money, the first payment is not due for 9 months. If he will make 24 monthly payments, how much interest is in the 17th payment? Answer=[ANS] dollars.", "answer_v3": [ "4.7008390204885" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0034", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "5", "keywords": [ "financial mathematics", "loans" ], "problem_v1": "Jessica owes 3300 dollars on a credit card that charges 1.5 percent interest per month. She decides to pay off the debt by making monthly payments of 85 dollars, starting one month from now, followed by a final smaller payment. How many payments, including the final one, will be required?\nAnswer=[ANS] payments.", "answer_v1": [ "59" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Jessica owes 2500 dollars on a credit card that charges 1.2 percent interest per month. She decides to pay off the debt by making monthly payments of 95 dollars, starting one month from now, followed by a final smaller payment. How many payments, including the final one, will be required?\nAnswer=[ANS] payments.", "answer_v2": [ "32" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Jessica owes 2750 dollars on a credit card that charges 1.3 percent interest per month. She decides to pay off the debt by making monthly payments of 85 dollars, starting one month from now, followed by a final smaller payment. How many payments, including the final one, will be required?\nAnswer=[ANS] payments.", "answer_v3": [ "43" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0035", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "5", "keywords": [ "financial mathematics", "loans" ], "problem_v1": "Kathleen takes out a 30-year mortgage of 310000 dollars, to be repaid with monthly payments, the first coming a month from now. If the nominal rate of interest is 9 percent convertible monthly, what is the total amount of interest that she'll pay over the life of the loan? Hint: The total interest paid is equal to the sum of all monthly payments minus the principal. Answer=[ANS] dollars.", "answer_v1": [ "587958.840510376" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Kathleen takes out a 30-year mortgage of 350000 dollars, to be repaid with monthly payments, the first coming a month from now. If the nominal rate of interest is 7.9 percent convertible monthly, what is the total amount of interest that she'll pay over the life of the loan? Hint: The total interest paid is equal to the sum of all monthly payments minus the principal. Answer=[ANS] dollars.", "answer_v2": [ "565774.810615951" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Kathleen takes out a 30-year mortgage of 310000 dollars, to be repaid with monthly payments, the first coming a month from now. If the nominal rate of interest is 8.3 percent convertible monthly, what is the total amount of interest that she'll pay over the life of the loan? Hint: The total interest paid is equal to the sum of all monthly payments minus the principal. Answer=[ANS] dollars.", "answer_v3": [ "532339.553936558" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0036", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "financial mathematics", "loans" ], "problem_v1": "Bill borrows 3300 dollars, to be repaid with 12 equal monthly payments, the first coming 6 months from now. If the rate of interest is 8.8 percent convertible monthly, what is Bill's monthly payment?\nAnswer=[ANS] dollars.", "answer_v1": [ "299.010485385457" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Bill borrows 2500 dollars, to be repaid with 12 equal monthly payments, the first coming 4 months from now. If the rate of interest is 9.8 percent convertible monthly, what is Bill's monthly payment?\nAnswer=[ANS] dollars.", "answer_v2": [ "224.980442246213" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Bill borrows 2750 dollars, to be repaid with 12 equal monthly payments, the first coming 5 months from now. If the rate of interest is 8.9 percent convertible monthly, what is Bill's monthly payment?\nAnswer=[ANS] dollars.", "answer_v3": [ "247.57457767355" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0037", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "financial mathematics", "yield rates" ], "problem_v1": "Norah borrows 17500 dollars from Zoie at a nominal rate of 6.9 percent convertible monthly, and agrees to make 20 equal monthly payments, the first coming in 9 months, to repay the loan. Immediately after Norah makes the 16th payment, Zoie sells the loan to Kate. If Kate's yield rate on the loan is 9 percent convertible monthly, how much did Kate pay Zoie for the loan? Answer=[ANS] dollars", "answer_v1": [ "3817.67540491381" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Norah borrows 10500 dollars from Zoie at a nominal rate of 7.5 percent convertible monthly, and agrees to make 20 equal monthly payments, the first coming in 9 months, to repay the loan. Immediately after Norah makes the 16th payment, Zoie sells the loan to Kate. If Kate's yield rate on the loan is 8.1 percent convertible monthly, how much did Kate pay Zoie for the loan? Answer=[ANS] dollars", "answer_v2": [ "2315.8277984408" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Norah borrows 13000 dollars from Zoie at a nominal rate of 6.9 percent convertible monthly, and agrees to make 20 equal monthly payments, the first coming in 9 months, to repay the loan. Immediately after Norah makes the 16th payment, Zoie sells the loan to Kate. If Kate's yield rate on the loan is 8.4 percent convertible monthly, how much did Kate pay Zoie for the loan? Answer=[ANS] dollars", "answer_v3": [ "2839.49636906048" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0038", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "financial mathematics", "yield rates" ], "problem_v1": "Jess borrows 4300 dollars from Wes at a rate of 8.6 percent convertible semiannually, and agrees to make 21 equal annual payments (the first a year from now) to repay the loan. Immediately after Jess makes the 6th payment, Wes sells the loan to Su. If Wes' total yield rate (on both the original loan and the sale to Su) is 3.6 percent effective, how much does Su pay Wes for the loan? Answer=[ANS] dollars.", "answer_v1": [ "2325.62561445819" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Jess borrows 2200 dollars from Wes at a rate of 9.6 percent convertible semiannually, and agrees to make 16 equal annual payments (the first a year from now) to repay the loan. Immediately after Jess makes the 5th payment, Wes sells the loan to Su. If Wes' total yield rate (on both the original loan and the sale to Su) is 3.3 percent effective, how much does Su pay Wes for the loan? Answer=[ANS] dollars.", "answer_v2": [ "1101.00579711614" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Jess borrows 2900 dollars from Wes at a rate of 8.8 percent convertible semiannually, and agrees to make 18 equal annual payments (the first a year from now) to repay the loan. Immediately after Jess makes the 5th payment, Wes sells the loan to Su. If Wes' total yield rate (on both the original loan and the sale to Su) is 3.8 percent effective, how much does Su pay Wes for the loan? Answer=[ANS] dollars.", "answer_v3": [ "1708.44579237583" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0039", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "financial mathematics", "yield rates" ], "problem_v1": "Suppose you take out a 28-year loan from C'ville Bank for 36000 dollars at an interest rate of 6 percent effective. To repay the loan, you agree to make equal annual payments, the first coming in one year. After making the 10th payment, you decide to refinance your loan. In particular, you want to reduce your annual payment to 1500 dollars for each of the remaining 18 payments, and then make a large final payment at the end of the original 28-year period to pay off the loan. (This payment will come immediately after the final 1500 dollar loan payment.) To save money for this large final payment, you plan to make equal annual deposits into an account at Richmond Bank earning 11.5 percent effective. These deposits will occur at the same time as the 1500 dollar loan payments, i.e. the first deposit will be one year after you refinance the loan, and the last will be at the time of your final loan payment. C'ville Bank will agree to your plan, provided that their yield rate for the ENTIRE loan is 6.9 percent effective. What will be the amount of each of the annual deposits to your account at Richmond Bank?\nAnswer=[ANS] dollars.", "answer_v1": [ "1130.8446305434" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose you take out a 22-year loan from C'ville Bank for 39000 dollars at an interest rate of 5.1 percent effective. To repay the loan, you agree to make equal annual payments, the first coming in one year. After making the 10th payment, you decide to refinance your loan. In particular, you want to reduce your annual payment to 1500 dollars for each of the remaining 12 payments, and then make a large final payment at the end of the original 22-year period to pay off the loan. (This payment will come immediately after the final 1500 dollar loan payment.) To save money for this large final payment, you plan to make equal annual deposits into an account at Richmond Bank earning 10.7 percent effective. These deposits will occur at the same time as the 1500 dollar loan payments, i.e. the first deposit will be one year after you refinance the loan, and the last will be at the time of your final loan payment. C'ville Bank will agree to your plan, provided that their yield rate for the ENTIRE loan is 7.8 percent effective. What will be the amount of each of the annual deposits to your account at Richmond Bank?\nAnswer=[ANS] dollars.", "answer_v2": [ "3127.44862802593" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose you take out a 24-year loan from C'ville Bank for 36000 dollars at an interest rate of 5.4 percent effective. To repay the loan, you agree to make equal annual payments, the first coming in one year. After making the 10th payment, you decide to refinance your loan. In particular, you want to reduce your annual payment to 1500 dollars for each of the remaining 14 payments, and then make a large final payment at the end of the original 24-year period to pay off the loan. (This payment will come immediately after the final 1500 dollar loan payment.) To save money for this large final payment, you plan to make equal annual deposits into an account at Richmond Bank earning 11.1 percent effective. These deposits will occur at the same time as the 1500 dollar loan payments, i.e. the first deposit will be one year after you refinance the loan, and the last will be at the time of your final loan payment. C'ville Bank will agree to your plan, provided that their yield rate for the ENTIRE loan is 6.9 percent effective. What will be the amount of each of the annual deposits to your account at Richmond Bank?\nAnswer=[ANS] dollars.", "answer_v3": [ "1651.74098605568" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0040", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "financial mathematics", "yield rates" ], "problem_v1": "Larry borrows 18600 dollars from Moe at an effective rate of 9.3 percent, and agrees to make 12 equal annual payments (the first a year from now) to repay the loan. Immediately after Larry makes the seventh payment, Moe sells the loan to Curly. If Moe's total yield rate is 6.2 percent effective, how much does Curly pay for the loan? Answer=[ANS] dollars.", "answer_v1": [ "6069.9521227438" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Larry borrows 17300 dollars from Moe at an effective rate of 8.5 percent, and agrees to make 12 equal annual payments (the first a year from now) to repay the loan. Immediately after Larry makes the seventh payment, Moe sells the loan to Curly. If Moe's total yield rate is 6.9 percent effective, how much does Curly pay for the loan? Answer=[ANS] dollars.", "answer_v2": [ "7276.91053371213" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Larry borrows 17700 dollars from Moe at an effective rate of 8.8 percent, and agrees to make 12 equal annual payments (the first a year from now) to repay the loan. Immediately after Larry makes the seventh payment, Moe sells the loan to Curly. If Moe's total yield rate is 6.2 percent effective, how much does Curly pay for the loan? Answer=[ANS] dollars.", "answer_v3": [ "6302.62942422897" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0041", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "financial mathematics", "yield rates" ], "problem_v1": "All the Peanuts characters pool their money to buy an Old House. They take out a 14 year mortgage for 87000 dollars at a rate of interest of 6 percent convertible monthly, agreeing to make equal monthly payments with the first due one month later. Immediately after making the 20th payment, they decide to hire Bob Villa to remodel their house. To do this, they will need to refinance their loan and also borrow an additional 100,000 dollars. They make a deal with the lender where they will pay off the balance owed (on the original loan plus the additional 100,000 dollars) with 21 more years of equal monthly payments. The lender agrees, provided that its yield rate on the ENTIRE LOAN is 9 percent convertible monthly. Under these new terms, what is their new monthly payment? Answer=[ANS] dollars.", "answer_v1": [ "1632.46095654165" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "All the Peanuts characters pool their money to buy an Old House. They take out a 10 year mortgage for 94000 dollars at a rate of interest of 5.1 percent convertible monthly, agreeing to make equal monthly payments with the first due one month later. Immediately after making the 20th payment, they decide to hire Bob Villa to remodel their house. To do this, they will need to refinance their loan and also borrow an additional 100,000 dollars. They make a deal with the lender where they will pay off the balance owed (on the original loan plus the additional 100,000 dollars) with 25 more years of equal monthly payments. The lender agrees, provided that its yield rate on the ENTIRE LOAN is 7.8 percent convertible monthly. Under these new terms, what is their new monthly payment? Answer=[ANS] dollars.", "answer_v2": [ "1408.63997869024" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "All the Peanuts characters pool their money to buy an Old House. They take out a 11 year mortgage for 87000 dollars at a rate of interest of 5.4 percent convertible monthly, agreeing to make equal monthly payments with the first due one month later. Immediately after making the 20th payment, they decide to hire Bob Villa to remodel their house. To do this, they will need to refinance their loan and also borrow an additional 100,000 dollars. They make a deal with the lender where they will pay off the balance owed (on the original loan plus the additional 100,000 dollars) with 21 more years of equal monthly payments. The lender agrees, provided that its yield rate on the ENTIRE LOAN is 8.4 percent convertible monthly. Under these new terms, what is their new monthly payment? Answer=[ANS] dollars.", "answer_v3": [ "1533.49032398068" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0042", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "financial mathematics", "yield rates" ], "problem_v1": "TJ has borrowed 7900 dollars at a nominal rate of interest of 5.7 percent convertible monthly. He has agreed to repay the loan with equal monthly payments for 5 years, the first coming one month after the loan is made. After making the 30th payment, he makes a deal with the lender where he'll pay off the balance owed on the loan with 36 more equal monthly payments. The lender agrees, provided that the yield rate on the remaining payments is 8.7 percent convertible monthly. Under these new terms, how large are TJ's new monthly payments? Answer=[ANS] dollars.", "answer_v1": [ "133.932513801435" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "TJ has borrowed 6325 dollars at a nominal rate of interest of 3.9 percent convertible monthly. He has agreed to repay the loan with equal monthly payments for 7 years, the first coming one month after the loan is made. After making the 30th payment, he makes a deal with the lender where he'll pay off the balance owed on the loan with 36 more equal monthly payments. The lender agrees, provided that the yield rate on the remaining payments is 7.2 percent convertible monthly. Under these new terms, how large are TJ's new monthly payments? Answer=[ANS] dollars.", "answer_v2": [ "131.96123411304" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "TJ has borrowed 7200 dollars at a nominal rate of interest of 4.5 percent convertible monthly. He has agreed to repay the loan with equal monthly payments for 4 years, the first coming one month after the loan is made. After making the 30th payment, he makes a deal with the lender where he'll pay off the balance owed on the loan with 36 more equal monthly payments. The lender agrees, provided that the yield rate on the remaining payments is 7.8 percent convertible monthly. Under these new terms, how large are TJ's new monthly payments? Answer=[ANS] dollars.", "answer_v3": [ "89.1280707092099" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0043", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "financial mathematics", "yield rates" ], "problem_v1": "Melissa borrows 18600 dollars from Western Maryland Bank at an effective rate of 9.3 percent, and agrees to make 15 annual payments (the first a year from now) to repay the loan. Immediately after Melissa makes the 9th payment, Western Maryland Bank sells the loan to McDaniel Bank. If Western Maryland Bank's total yield rate (on both the original loan and the sale to McDaniel Bank) is 6.2 percent, how much does McDaniel Bank pay for the loan? Answer=[ANS] dollars.", "answer_v1": [ "4750.03913681093" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Melissa borrows 17300 dollars from Western Maryland Bank at an effective rate of 8.5 percent, and agrees to make 15 annual payments (the first a year from now) to repay the loan. Immediately after Melissa makes the 9th payment, Western Maryland Bank sells the loan to McDaniel Bank. If Western Maryland Bank's total yield rate (on both the original loan and the sale to McDaniel Bank) is 6.9 percent, how much does McDaniel Bank pay for the loan? Answer=[ANS] dollars.", "answer_v2": [ "6688.88797688861" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Melissa borrows 17700 dollars from Western Maryland Bank at an effective rate of 8.8 percent, and agrees to make 15 annual payments (the first a year from now) to repay the loan. Immediately after Melissa makes the 9th payment, Western Maryland Bank sells the loan to McDaniel Bank. If Western Maryland Bank's total yield rate (on both the original loan and the sale to McDaniel Bank) is 6.2 percent, how much does McDaniel Bank pay for the loan? Answer=[ANS] dollars.", "answer_v3": [ "5272.12943324375" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0044", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "financial mathematics", "yield rates" ], "problem_v1": "Schroeder borrows 8600 dollars from Peppermint Patty at an effective rate of 4.3 percent, and agrees to make 12 equal annual payments (the first one year later) to repay the loan. Immediately after she receives the 5th payment, Peppermint Patty sells the loan to Franklin at a price that will provide Franklin with a yield of 7.1 percent effective. How much does Franklin pay for the loan? Answer=[ANS] dollars.", "answer_v1": [ "5007.3411808554" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Schroeder borrows 7300 dollars from Peppermint Patty at an effective rate of 2.2 percent, and agrees to make 9 equal annual payments (the first one year later) to repay the loan. Immediately after she receives the 5th payment, Peppermint Patty sells the loan to Franklin at a price that will provide Franklin with a yield of 7.5 percent effective. How much does Franklin pay for the loan? Answer=[ANS] dollars.", "answer_v2": [ "3024.17525265168" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Schroeder borrows 7700 dollars from Peppermint Patty at an effective rate of 2.9 percent, and agrees to make 10 equal annual payments (the first one year later) to repay the loan. Immediately after she receives the 5th payment, Peppermint Patty sells the loan to Franklin at a price that will provide Franklin with a yield of 7.1 percent effective. How much does Franklin pay for the loan? Answer=[ANS] dollars.", "answer_v3": [ "3672.44319029675" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0045", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "financial mathematics", "yield rates" ], "problem_v1": "Fred takes out a loan from C'Ville Bank at a nominal rate of 10.2 percent convertible monthly, and agrees to repay the loan with 36 equal monthly payments, the first due a month after the loan is made. Immediately after making the 13th payment, C'Ville sells the loan to Richmond Bank for 2300 dollars. If Richmond Bank's yield on the loan is 14.4 percent convertible monthly, how much did Fred originally borrow? Answer=[ANS] dollars", "answer_v1": [ "3554.53919199901" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Fred takes out a loan from C'Ville Bank at a nominal rate of 10.8 percent convertible monthly, and agrees to repay the loan with 36 equal monthly payments, the first due a month after the loan is made. Immediately after making the 13th payment, C'Ville sells the loan to Richmond Bank for 2000 dollars. If Richmond Bank's yield on the loan is 13.5 percent convertible monthly, how much did Fred originally borrow? Answer=[ANS] dollars", "answer_v2": [ "3038.12020124167" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Fred takes out a loan from C'Ville Bank at a nominal rate of 10.2 percent convertible monthly, and agrees to repay the loan with 36 equal monthly payments, the first due a month after the loan is made. Immediately after making the 13th payment, C'Ville sells the loan to Richmond Bank for 2100 dollars. If Richmond Bank's yield on the loan is 13.5 percent convertible monthly, how much did Fred originally borrow? Answer=[ANS] dollars", "answer_v3": [ "3217.91507938722" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0046", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "financial mathematics", "yield rates" ], "problem_v1": "Gonzo borrows 22000 dollars from Kermit at an effective rate of 9.3 percent, and agrees to make 18 equal annual payments (the first a year from now) to repay the loan. Immediately after Gonzo makes the 4th payment, Kermit sells the loan to Fozzie. If Kermit's total yield rate (on both the original loan and the sale to Fozzie) is 3.2 percent effective, how much did Fozzie pay for the loan? Answer=[ANS] dollars.", "answer_v1": [ "14198.8011374073" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Gonzo borrows 18200 dollars from Kermit at an effective rate of 8.5 percent, and agrees to make 15 equal annual payments (the first a year from now) to repay the loan. Immediately after Gonzo makes the 6th payment, Kermit sells the loan to Fozzie. If Kermit's total yield rate (on both the original loan and the sale to Fozzie) is 3.9 percent effective, how much did Fozzie pay for the loan? Answer=[ANS] dollars.", "answer_v2": [ "8395.58478032194" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Gonzo borrows 19200 dollars from Kermit at an effective rate of 8.8 percent, and agrees to make 17 equal annual payments (the first a year from now) to repay the loan. Immediately after Gonzo makes the 4th payment, Kermit sells the loan to Fozzie. If Kermit's total yield rate (on both the original loan and the sale to Fozzie) is 3.2 percent effective, how much did Fozzie pay for the loan? Answer=[ANS] dollars.", "answer_v3": [ "12469.0257750289" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0047", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "financial mathematics", "yield rates" ], "problem_v1": "Paolo borrows 18800 dollars from Anna at an effective rate of 9.1 percent, and agrees to make 19 equal annual payments (the first a year from now) to repay the loan. Immediately after Paolo makes the 11th payment, Anna sells the loan to Carlo. If Anna's total yield rate (on both the original loan and the sale to Carlo) is 6.3 percent effective, how much does Carlo pay Anna for the loan? Answer=[ANS] dollars.", "answer_v1": [ "4644.66018372213" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Paolo borrows 17800 dollars from Anna at an effective rate of 9.5 percent, and agrees to make 14 equal annual payments (the first a year from now) to repay the loan. Immediately after Paolo makes the 11th payment, Anna sells the loan to Carlo. If Anna's total yield rate (on both the original loan and the sale to Carlo) is 5.3 percent effective, how much does Carlo pay Anna for the loan? Answer=[ANS] dollars.", "answer_v2": [ "-2511.01135835563" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Paolo borrows 18400 dollars from Anna at an effective rate of 9.1 percent, and agrees to make 16 equal annual payments (the first a year from now) to repay the loan. Immediately after Paolo makes the 11th payment, Anna sells the loan to Carlo. If Anna's total yield rate (on both the original loan and the sale to Carlo) is 5.5 percent effective, how much does Carlo pay Anna for the loan? Answer=[ANS] dollars.", "answer_v3": [ "678.252086527551" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0048", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "algebra" ], "problem_v1": "Debbie bought a new computer for \\$1800. She will pay it off by making annual payments of \\$130. The store charges $4\\%$ interest rate, compounded annually. How long will it take Debbie to pay off the computer? [ANS] years.", "answer_v1": [ "20.5781938934897" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Debbie bought a new computer for \\$1000. She will pay it off by making annual payments of \\$150. The store charges $2\\%$ interest rate, compounded annually. How long will it take Debbie to pay off the computer? [ANS] years.", "answer_v2": [ "7.22635645767468" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Debbie bought a new computer for \\$1300. She will pay it off by making annual payments of \\$135. The store charges $3\\%$ interest rate, compounded annually. How long will it take Debbie to pay off the computer? [ANS] years.", "answer_v3": [ "11.5338430896035" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0049", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "Mr. Smith is purchasing a \\$ 180000 house. The down payment is 20 \\% of the price of the house. He is given the choice of two mortgages:\na) a 25-year mortgage at a rate of 9 \\%. Find (i) the monthly payment: \\$ [ANS]\n(ii) the total amount of interest paid: \\$ [ANS]\nb) a 15-year mortgage at a rate of 9 \\%. Find (i) The monthly payment: \\$ [ANS]\n(ii) the total amount of interest paid: \\$ [ANS]", "answer_v1": [ "1208.44276363417", "218532.829090252", "1460.54388119296", "118897.898614734" ], "answer_type_v1": [ "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [] ], "problem_v2": "Mr. Smith is purchasing a \\$ 90000 house. The down payment is 20 \\% of the price of the house. He is given the choice of two mortgages:\na) a 30-year mortgage at a rate of 6 \\%. Find (i) the monthly payment: \\$ [ANS]\n(ii) the total amount of interest paid: \\$ [ANS]\nb) a 15-year mortgage at a rate of 6 \\%. Find (i) The monthly payment: \\$ [ANS]\n(ii) the total amount of interest paid: \\$ [ANS]", "answer_v2": [ "431.676378109985", "83403.4961195946", "607.576916194893", "37363.8449150807" ], "answer_type_v2": [ "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [] ], "problem_v3": "Mr. Smith is purchasing a \\$ 120000 house. The down payment is 20 \\% of the price of the house. He is given the choice of two mortgages:\na) a 25-year mortgage at a rate of 7 \\%. Find (i) the monthly payment: \\$ [ANS]\n(ii) the total amount of interest paid: \\$ [ANS]\nb) a 15-year mortgage at a rate of 7 \\%. Find (i) The monthly payment: \\$ [ANS]\n(ii) the total amount of interest paid: \\$ [ANS]", "answer_v3": [ "678.508029384087", "107552.408815226", "862.875140018328", "59317.525203299" ], "answer_type_v3": [ "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [] ] }, { "id": "Financial_mathematics_0050", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "percent", "mathematics for business", "algebraic expression", "compound interest", "financial mathematics" ], "problem_v1": "Stereo Inc. sells a stereo system for \\$500 down and monthly payments of \\$70 for the next 4 years. If the interest rate is 2.75\\% per month, find:\na) The cost of the stereo. Answer=\\$ [ANS]\nb) The total amount of interest paid. Answer=\\$ [ANS]", "answer_v1": [ "2353.24516571995", "1506.75483428005" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Stereo Inc. sells a stereo system for \\$100 down and monthly payments of \\$90 for the next 2 years. If the interest rate is 2\\% per month, find:\na) The cost of the stereo. Answer=\\$ [ANS]\nb) The total amount of interest paid. Answer=\\$ [ANS]", "answer_v2": [ "1802.2533042752", "457.7466957248" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Stereo Inc. sells a stereo system for \\$200 down and monthly payments of \\$70 for the next 3 years. If the interest rate is 2.25\\% per month, find:\na) The cost of the stereo. Answer=\\$ [ANS]\nb) The total amount of interest paid. Answer=\\$ [ANS]", "answer_v3": [ "1914.62660549656", "805.373394503439" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0051", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "Find the monthly payment needed to pay off a loan of \\$3500 amortized at 11\\% compounded monthly for 4 years.\nMonthly payment=\\$ [ANS]", "answer_v1": [ "90.459329140084" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Find the monthly payment needed to pay off a loan of \\$2100 amortized at 4\\% compounded monthly for 6 years.\nMonthly payment=\\$ [ANS]", "answer_v2": [ "32.8548844523386" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Find the monthly payment needed to pay off a loan of \\$2600 amortized at 6\\% compounded monthly for 5 years.\nMonthly payment=\\$ [ANS]", "answer_v3": [ "50.2652839765135" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0052", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "5", "keywords": [ "percent" ], "problem_v1": "Mr. Smith bought a \\$ 430000 house 8 years ago. The house is now worth \\$ 645000. Originally, the house was financed by paying 15\\% down with the rest financed through a 25-year mortgage at 9\\% interest. After making 96 monthly house payments,Mr. Smith is now in need of cash, and would like to refinance the house. The finance company is willing to loan 95\\% of the current value of the house amortized over 25 years at 5\\% interest. How much cash will the owner receive after paying the balance of the original loan?\nAmount of cash obtained=\\$ [ANS]\nIf he uses all of the available cash for something other than investing in his home, by how much will his monthly payment increase?\nIncrease in monthly payment=\\$ [ANS]", "answer_v1": [ "292844.886831374", "514.812770254802" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Mr. Smith bought a \\$ 220000 house 10 years ago. The house is now worth \\$ 440000. Originally, the house was financed by paying 15\\% down with the rest financed through a 15-year mortgage at 7\\% interest. After making 120 monthly house payments,Mr. Smith is now in need of cash, and would like to refinance the house. The finance company is willing to loan 85\\% of the current value of the house amortized over 20 years at 5\\% interest. How much cash will the owner receive after paying the balance of the original loan?\nAmount of cash obtained=\\$ [ANS]\nIf he uses all of the available cash for something other than investing in his home, by how much will his monthly payment increase?\nIncrease in monthly payment=\\$ [ANS]", "answer_v2": [ "289115.801547618", "787.425598176269" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Mr. Smith bought a \\$ 290000 house 8 years ago. The house is now worth \\$ 406000. Originally, the house was financed by paying 20\\% down with the rest financed through a 20-year mortgage at 12\\% interest. After making 96 monthly house payments,Mr. Smith is now in need of cash, and would like to refinance the house. The finance company is willing to loan 105\\% of the current value of the house amortized over 25 years at 11\\% interest. How much cash will the owner receive after paying the balance of the original loan?\nAmount of cash obtained=\\$ [ANS]\nIf he uses all of the available cash for something other than investing in his home, by how much will his monthly payment increase?\nIncrease in monthly payment=\\$ [ANS]", "answer_v3": [ "231806.121443627", "1623.7022170146" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0053", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "percent" ], "problem_v1": "Sheds R Us sells \\$700 sheds on a monthly payment plan over 4 years. a) If the interest rate is 2.75\\% per month, find the monthly payment. Answer=\\$ [ANS]\nb) If instead the interest rate is 3\\% per month, find the monthly payment Answer=\\$ [ANS]", "answer_v1": [ "26.4401067416056", "27.7044416635358" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Sheds R Us sells \\$900 sheds on a monthly payment plan over 2 years. a) If the interest rate is 2\\% per month, find the monthly payment. Answer=\\$ [ANS]\nb) If instead the interest rate is 2.25\\% per month, find the monthly payment Answer=\\$ [ANS]", "answer_v2": [ "47.5839875279249", "48.9422060156503" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Sheds R Us sells \\$700 sheds on a monthly payment plan over 3 years. a) If the interest rate is 2.25\\% per month, find the monthly payment. Answer=\\$ [ANS]\nb) If instead the interest rate is 2.5\\% per month, find the monthly payment Answer=\\$ [ANS]", "answer_v3": [ "28.577650575887", "29.7161037204379" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0054", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "5", "keywords": [ "exponential model", "credit card" ], "problem_v1": "Dom has a credit card with an outstanding balance of \\$19,908. The credit card company charges an APR (annual percentage rate) of 22.6\\% compounded montly. The minimum payment is \\$517 per month. If Dom makes no new charges on the credit card while making only the mininum monthly payment\n(a) How many months will it take to pay off the outstanding balance? Answer: [ANS]\n(b) How much total interest will Dom have paid after his last payment of \\$517? Answer: \\$ [ANS]\n(c) What monthly payment is necessary to repay the debt in 1 years? Answer: \\$ [ANS]", "answer_v1": [ "70", "16282", "1869.03041866905" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Jake has a credit card with an outstanding balance of \\$21,659. The credit card company charges an APR (annual percentage rate) of 20.7\\% compounded montly. The minimum payment is \\$476 per month. If Jake makes no new charges on the credit card while making only the mininum monthly payment\n(a) How many months will it take to pay off the outstanding balance? Answer: [ANS]\n(b) How much total interest will Jake have paid after his last payment of \\$476? Answer: \\$ [ANS]\n(c) What monthly payment is necessary to repay the debt in 3 years? Answer: \\$ [ANS]", "answer_v2": [ "90", "21181", "812.671921660933" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "David has a credit card with an outstanding balance of \\$20,027. The credit card company charges an APR (annual percentage rate) of 21.7\\% compounded montly. The minimum payment is \\$460 per month. If David makes no new charges on the credit card while making only the mininum monthly payment\n(a) How many months will it take to pay off the outstanding balance? Answer: [ANS]\n(b) How much total interest will David have paid after his last payment of \\$460? Answer: \\$ [ANS]\n(c) What monthly payment is necessary to repay the debt in 1 years? Answer: \\$ [ANS]", "answer_v3": [ "87", "19993", "1871.52430189834" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Financial_mathematics_0055", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [], "problem_v1": "Wilbur has a loan with an effective interest rate of 12 \\% per year. He makes payments at the end of each year for 10 years. The first payment is \\$ 200, and each subsequent payment increases by \\$ 15 per year. Calculate the interest portion of the fourth payment.\nThe interest portion of the fourth payment=\\$ [ANS]?", "answer_v1": [ "155.13" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Wilbur has a loan with an effective interest rate of 4 \\% per year. He makes payments at the end of each year for 10 years. The first payment is \\$ 200, and each subsequent payment increases by \\$ 25 per year. Calculate the interest portion of the second payment.\nThe interest portion of the second payment=\\$ [ANS]?", "answer_v2": [ "94.72" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Wilbur has a loan with an effective interest rate of 7 \\% per year. He makes payments at the end of each year for 10 years. The first payment is \\$ 200, and each subsequent payment increases by \\$ 20 per year. Calculate the interest portion of the third payment.\nThe interest portion of the third payment=\\$ [ANS]?", "answer_v3": [ "126.62" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0056", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "5", "keywords": [ "extra payment", "loan balance" ], "problem_v1": "Nick purchased Natalie's engagement ring on January 1, 2004 with a \\$ 10,000 loan. His loan carries an interest rate of 17 \\% per year convertible monthly. He pays \\$ 900 per month starting February 1, 2004, plus an additional \\$ 1950 on August 1, 2004. His last payment will be a partial payment. Determine for how many months he will be making loan payments, counting the last partial payment.\nTotal number of months=[ANS]?", "answer_v1": [ "10" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Nick purchased Natalie's engagement ring on January 1, 2004 with a \\$ 10,000 loan. His loan carries an interest rate of 6 \\% per year convertible monthly. He pays \\$ 1150 per month starting February 1, 2004, plus an additional \\$ 2200 on August 1, 2004. His last payment will be a partial payment. Determine for how many months he will be making loan payments, counting the last partial payment.\nTotal number of months=[ANS]?", "answer_v2": [ "7" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Nick purchased Natalie's engagement ring on January 1, 2004 with a \\$ 10,000 loan. His loan carries an interest rate of 10 \\% per year convertible monthly. He pays \\$ 950 per month starting February 1, 2004, plus an additional \\$ 2000 on August 1, 2004. His last payment will be a partial payment. Determine for how many months he will be making loan payments, counting the last partial payment.\nTotal number of months=[ANS]?", "answer_v3": [ "9" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0057", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "5", "keywords": [ "missed payment", "loan balance" ], "problem_v1": "Allan borrowed \\$ 280000 on January 1, 1976, which was to be repaid in 360 level monthly installments at a nominal annual interest rate of 12 \\% convertible monthly. The first monthly payment was due February 1, 1976. Allan missed the first payment, but began making payments on March 1, 1976, and he made 359 payments. Determine how much Allan owed on the loan after making his 359-th payment.\nHow much was owed after the 359-th payment=\\$ [ANS]?", "answer_v1": [ "102510" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Allan borrowed \\$ 380000 on January 1, 1976, which was to be repaid in 360 level monthly installments at a nominal annual interest rate of 3 \\% convertible monthly. The first monthly payment was due February 1, 1976. Allan missed the first payment, but began making payments on March 1, 1976, and he made 359 payments. Determine how much Allan owed on the loan after making his 359-th payment.\nHow much was owed after the 359-th payment=\\$ [ANS]?", "answer_v2": [ "3926" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Allan borrowed \\$ 280000 on January 1, 1976, which was to be repaid in 360 level monthly installments at a nominal annual interest rate of 6 \\% convertible monthly. The first monthly payment was due February 1, 1976. Allan missed the first payment, but began making payments on March 1, 1976, and he made 359 payments. Determine how much Allan owed on the loan after making his 359-th payment.\nHow much was owed after the 359-th payment=\\$ [ANS]?", "answer_v3": [ "10060" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0058", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "monthly payment" ], "problem_v1": "A loan of \\$ 10500 is to be repaid in 39 equal monthly installments with the first one paid seven months after the loan is made. The nominal annual interest rate is 10 \\% compounded semiannually. Determine the amount of the monthly payment.\nAmount of monthly payment=\\$ [ANS]?", "answer_v1": [ "331.23" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A loan of \\$ 6500 is to be repaid in 27 equal monthly installments with the first one paid seven months after the loan is made. The nominal annual interest rate is 15 \\% compounded quarterly. Determine the amount of the monthly payment.\nAmount of monthly payment=\\$ [ANS]?", "answer_v2": [ "306.31" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A loan of \\$ 8000 is to be repaid in 30 equal monthly installments with the first one paid seven months after the loan is made. The nominal annual interest rate is 10 \\% compounded quarterly. Determine the amount of the monthly payment.\nAmount of monthly payment=\\$ [ANS]?", "answer_v3": [ "317.48" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0059", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [ "present value" ], "problem_v1": "On January 1, 2000, Matt has the following two options for repaying a loan:\ni) Sixty monthly payments of \\$ 100 beginning February 1, 2000. ii) A single payment of \\$ 6500 at the end of K months.\nInterest is at a nominal annual rate of 12 \\% compounded quarterly. The two options have the same present value. Determine K. (Round to the nearest integer.)\nK=[ANS] months.", "answer_v1": [ "37" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "On January 1, 2000, Matt has the following two options for repaying a loan:\ni) Sixty monthly payments of \\$ 100 beginning February 1, 2000. ii) A single payment of \\$ 6900 at the end of K months.\nInterest is at a nominal annual rate of 3 \\% compounded bimonthly. The two options have the same present value. Determine K. (Round to the nearest integer.)\nK=[ANS] months.", "answer_v2": [ "86" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "On January 1, 2000, Matt has the following two options for repaying a loan:\ni) Sixty monthly payments of \\$ 100 beginning February 1, 2000. ii) A single payment of \\$ 6500 at the end of K months.\nInterest is at a nominal annual rate of 6 \\% compounded bimonthly. The two options have the same present value. Determine K. (Round to the nearest integer.)\nK=[ANS] months.", "answer_v3": [ "46" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0060", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "5", "keywords": [ "unknown interest rate", "present value" ], "problem_v1": "A renter with \\$ 1136.76 has a one year lease. The landlord is willing to accept two payment options: i) \\$ 1136.76 now, or ii) \\$ 100 at the beginning of each month for twelve months. What nominal annual interest rate compounded monthly would be required for the two options to have the same present value?\nAnnual nominal interest rate=[ANS] \\%?", "answer_v1": [ "12" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A renter with \\$ 1183.68 has a one year lease. The landlord is willing to accept two payment options: i) \\$ 1183.68 now, or ii) \\$ 100 at the beginning of each month for twelve months. What nominal annual interest rate compounded monthly would be required for the two options to have the same present value?\nAnnual nominal interest rate=[ANS] \\%?", "answer_v2": [ "3" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A renter with \\$ 1167.7 has a one year lease. The landlord is willing to accept two payment options: i) \\$ 1167.7 now, or ii) \\$ 100 at the beginning of each month for twelve months. What nominal annual interest rate compounded monthly would be required for the two options to have the same present value?\nAnnual nominal interest rate=[ANS] \\%?", "answer_v3": [ "6" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0061", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "5", "keywords": [], "problem_v1": "A loan is to amortized by n level annual payments of X, where $n\\ge 6$. You are given: i) The amount of interest in the first payment is \\$ 789.17. ii) The amount of interest in the third payment is \\$ 759.16. iii) The amount of interest in the fifth payment is \\$ 721.51. Calculate X. Annual payment X=\\$ [ANS]?", "answer_v1": [ "907" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A loan is to amortized by n level annual payments of X, where $n\\ge 6$. You are given: i) The amount of interest in the first payment is \\$ 310.29. ii) The amount of interest in the third payment is \\$ 241.6. iii) The amount of interest in the fifth payment is \\$ 167.29. Calculate X. Annual payment X=\\$ [ANS]?", "answer_v2": [ "1152" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A loan is to amortized by n level annual payments of X, where $n\\ge 6$. You are given: i) The amount of interest in the first payment is \\$ 484.91. ii) The amount of interest in the third payment is \\$ 421.31. iii) The amount of interest in the fifth payment is \\$ 348.5. Calculate X. Annual payment X=\\$ [ANS]?", "answer_v3": [ "924" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0062", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [], "problem_v1": "A loan of \\$ 10,000 is amortized by equal annual payments for 30 years at an effective annual interest rate of 12 \\%. Determine the year in which the interest portion of the payment is most nearly equal to one-fourth of the payment.\nThe year that the interest portion of payment is most nearly equal to one-fourth of the payment=[ANS]?", "answer_v1": [ "28" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A loan of \\$ 10,000 is amortized by equal annual payments for 30 years at an effective annual interest rate of 4 \\%. Determine the year in which the interest portion of the payment is most nearly equal to one-fifth of the payment.\nThe year that the interest portion of payment is most nearly equal to one-fifth of the payment=[ANS]?", "answer_v2": [ "25" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A loan of \\$ 10,000 is amortized by equal annual payments for 30 years at an effective annual interest rate of 7 \\%. Determine the year in which the interest portion of the payment is most nearly equal to one-fourth of the payment.\nThe year that the interest portion of payment is most nearly equal to one-fourth of the payment=[ANS]?", "answer_v3": [ "27" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0063", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "5", "keywords": [ "varying payments", "loan amount", "present value", "increasing payments" ], "problem_v1": "Sharon buys a house. She has limited initial funds, so she agrees to make 360 monthly payments as follows: The first payment is to be \\$ 800, with each subsequent payment increasing by \\$ 11. The first payment is due one month after the date of the loan. The nominal annual interest rate is 9 \\% compounded monthly. Determine how much Sharon borrowed. How much did Sharon borrow=\\$ [ANS]?", "answer_v1": [ "245861.75" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Sharon buys a house. She has limited initial funds, so she agrees to make 360 monthly payments as follows: The first payment is to be \\$ 450, with each subsequent payment increasing by \\$ 15. The first payment is due one month after the date of the loan. The nominal annual interest rate is 3 \\% compounded monthly. Determine how much Sharon borrowed. How much did Sharon borrow=\\$ [ANS]?", "answer_v2": [ "650694.17" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Sharon buys a house. She has limited initial funds, so she agrees to make 360 monthly payments as follows: The first payment is to be \\$ 550, with each subsequent payment increasing by \\$ 11. The first payment is due one month after the date of the loan. The nominal annual interest rate is 5 \\% compounded monthly. Determine how much Sharon borrowed. How much did Sharon borrow=\\$ [ANS]?", "answer_v3": [ "381513.56" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0064", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "5", "keywords": [ "missed payments", "loan balance" ], "problem_v1": "Sandra takes out a \\$ 28000 loan to be paid back in monthly payments of P over the next five years. The nominal interest rate is 12 \\% compounded monthly. After making the first payment one month from the date of the loan, she begins a habit of skipping two monthly payments after each payment of P. Determine the loan balance five years after taking out the loan.\nLoan balance after years=\\$ [ANS]?", "answer_v1": [ "33742.68" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Sandra takes out a \\$ 38000 loan to be paid back in monthly payments of P over the next five years. The nominal interest rate is 3 \\% compounded monthly. After making the first payment one month from the date of the loan, she begins a habit of skipping two monthly payments after each payment of P. Determine the loan balance five years after taking out the loan.\nLoan balance after years=\\$ [ANS]?", "answer_v2": [ "29390.87" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Sandra takes out a \\$ 28000 loan to be paid back in monthly payments of P over the next five years. The nominal interest rate is 6 \\% compounded monthly. After making the first payment one month from the date of the loan, she begins a habit of skipping two monthly payments after each payment of P. Determine the loan balance five years after taking out the loan.\nLoan balance after years=\\$ [ANS]?", "answer_v3": [ "25115.69" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0065", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "5", "keywords": [ "saving account", "down payment", "monthly payment" ], "problem_v1": "Nick has been depositing \\$ 160 in a savings account every three months for the past three years. This account paid 12 \\% convertible quarterly. Nick has just made the last deposit. Nick is buying a car for \\$ 17000. He is taking out a car loan. He will use the accumulated value of his savings account as the downpayment on the car. The loan is at 6 \\% convertible bimonthly and has a term of 5 years. Find the size of Nick's monthly car loan payment.\nNick's monthly car payment=\\$ [ANS]?", "answer_v1": [ "284.66" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Nick has been depositing \\$ 200 in a savings account every three months for the past three years. This account paid 3 \\% convertible bimonthly. Nick has just made the last deposit. Nick is buying a car for \\$ 10000. He is taking out a car loan. He will use the accumulated value of his savings account as the downpayment on the car. The loan is at 6 \\% convertible semiannually and has a term of 3 years. Find the size of Nick's monthly car loan payment.\nNick's monthly car payment=\\$ [ANS]?", "answer_v2": [ "227.86" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Nick has been depositing \\$ 160 in a savings account every three months for the past three years. This account paid 6 \\% convertible quarterly. Nick has just made the last deposit. Nick is buying a car for \\$ 12000. He is taking out a car loan. He will use the accumulated value of his savings account as the downpayment on the car. The loan is at 6 \\% convertible monthly and has a term of 6 years. Find the size of Nick's monthly car loan payment.\nNick's monthly car payment=\\$ [ANS]?", "answer_v3": [ "164.29" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0066", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "3", "keywords": [ "interest" ], "problem_v1": "Fifteen years ago a couple purchased a house for $\\\\$220{,}000.00$ by paying a 20\\% down payment and financing the remaining balance with a 30-year mortgage at $6.48$ \\% compounded monthly.\n(a) Find the monthly payment for this loan. Monthly Payment: $[ANS] (b) Find the balance of the loan after $17$ years and after $18$ years?\n$\\begin{array}{cccc}\\hline After 17 years & & After 18 years & \\\\\\hline n=& [ANS] & n=& [ANS] \\\\\\hlineLoan Balance: & $[ANS] & Loan Balance: & $[ANS] \\\\\\hline\\end{array}$ (Note: The balance amounts should include a dollar sign and be accurate to two decimal places) (c) Find the total amount of interest paid by the couple during the 18th year. Interest Paid During 18th year: $[ANS]", "answer_v1": [ "1110.13", "156", "144", "116840.16", "110916.00", "7397.35" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [], [] ], "problem_v2": "Fifteen years ago a couple purchased a house for $\\\\$110{,}000.00$ by paying a 20\\% down payment and financing the remaining balance with a 30-year mortgage at $4.6$ \\% compounded monthly.\n(a) Find the monthly payment for this loan. Monthly Payment: $[ANS] (b) Find the balance of the loan after $19$ years and after $20$ years?\n$\\begin{array}{cccc}\\hline After 19 years & & After 20 years & \\\\\\hline n=& [ANS] & n=& [ANS] \\\\\\hlineLoan Balance: & $[ANS] & Loan Balance: & $[ANS] \\\\\\hline\\end{array}$ (Note: The balance amounts should include a dollar sign and be accurate to two decimal places) (c) Find the total amount of interest paid by the couple during the 20th year. Interest Paid During 20th year: $[ANS]", "answer_v2": [ "451.13", "132", "120", "46663.89", "43327.14", "2076.77" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [], [] ], "problem_v3": "Fifteen years ago a couple purchased a house for $\\\\$150{,}000.00$ by paying a 20\\% down payment and financing the remaining balance with a 30-year mortgage at $5.12$ \\% compounded monthly.\n(a) Find the monthly payment for this loan. Monthly Payment: $[ANS] (b) Find the balance of the loan after $17$ years and after $18$ years?\n$\\begin{array}{cccc}\\hline After 17 years & & After 18 years & \\\\\\hline n=& [ANS] & n=& [ANS] \\\\\\hlineLoan Balance: & $[ANS] & Loan Balance: & $[ANS] \\\\\\hline\\end{array}$ (Note: The balance amounts should include a dollar sign and be accurate to two decimal places) (c) Find the total amount of interest paid by the couple during the 18th year. Interest Paid During 18th year: $[ANS]", "answer_v3": [ "653.02", "156", "144", "74276.41", "70147.17", "3706.95" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [], [] ] }, { "id": "Financial_mathematics_0067", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "3", "keywords": [ "financial mathematics", "interest", "present value" ], "problem_v1": "Rich buys a car for $\\\\$32{,}000$ and has two options for financing. The dealership offers either financing of $0$ \\% compounded monthly for 5-years, or a $\\\\$5{,}000$ cash rebate. If Rich takes the rebate, then he will apply the rebate to the cost of the car and finance the remaining balance with a loan for 5-years at $4.3$ \\% compounded monthly through the Tiger's Credit Union.\n(a) What would Rich's monthly payment be if he takes the 5-year $0$ \\% financing? Monthly payment for 5-year $0$ \\% financing=$[ANS]\n (b) What would Rich's monthly payment be if he takes the $\\\\$5{,}000$ rebate? Monthly payment with $\\\\$5{,}000$ rebate=$[ANS]\n (c) Which of the two options is financially better for Rich? Enter either \"1\" (for Option 1) if the $0$ \\% financing is better or enter \"2\" (for Option 2) if the $\\\\$5{,}000$ rebate is better. (Do not include the quotation marks in your answer.) Best Option is Option [ANS]", "answer_v1": [ "533.33", "500.91", "2" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Rich buys a car for $\\\\$20{,}000$ and has two options for financing. The dealership offers either financing of $0$ \\% compounded monthly for 5-years, or a $\\\\$5{,}000$ cash rebate. If Rich takes the rebate, then he will apply the rebate to the cost of the car and finance the remaining balance with a loan for 5-years at $5.35$ \\% compounded monthly through the Tiger's Credit Union.\n(a) What would Rich's monthly payment be if he takes the 5-year $0$ \\% financing? Monthly payment for 5-year $0$ \\% financing=$[ANS]\n (b) What would Rich's monthly payment be if he takes the $\\\\$5{,}000$ rebate? Monthly payment with $\\\\$5{,}000$ rebate=$[ANS]\n (c) Which of the two options is financially better for Rich? Enter either \"1\" (for Option 1) if the $0$ \\% financing is better or enter \"2\" (for Option 2) if the $\\\\$5{,}000$ rebate is better. (Do not include the quotation marks in your answer.) Best Option is Option [ANS]", "answer_v2": [ "333.33", "285.48", "2" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Rich buys a car for $\\\\$24{,}000$ and has two options for financing. The dealership offers either financing of $0$ \\% compounded monthly for 5-years, or a $\\\\$5{,}000$ cash rebate. If Rich takes the rebate, then he will apply the rebate to the cost of the car and finance the remaining balance with a loan for 5-years at $4.3$ \\% compounded monthly through the Tiger's Credit Union.\n(a) What would Rich's monthly payment be if he takes the 5-year $0$ \\% financing? Monthly payment for 5-year $0$ \\% financing=$[ANS]\n (b) What would Rich's monthly payment be if he takes the $\\\\$5{,}000$ rebate? Monthly payment with $\\\\$5{,}000$ rebate=$[ANS]\n (c) Which of the two options is financially better for Rich? Enter either \"1\" (for Option 1) if the $0$ \\% financing is better or enter \"2\" (for Option 2) if the $\\\\$5{,}000$ rebate is better. (Do not include the quotation marks in your answer.) Best Option is Option [ANS]", "answer_v3": [ "400", "352.49", "2" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Financial_mathematics_0068", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "5", "keywords": [ "financial mathematics", "interest", "present value", "loans" ], "problem_v1": "Starting on July 1, 2000, Peter borrows $\\\\$8{,}200.00$ each year for 4 years from his dear Aunt May to pay for college. (Note: the last date that he borrows money is July 1, 2003.) From the beginning, Aunt May agreed to defer all interest on the loans until Peter finds a job; i.e. Peter's loans will not accumulate any interest until the first day he starts working. After that, Peter will be charged 8.8 percent compounded semiannually, and he will pay Aunt May back with 16 equal semiannual payments, the first coming 6 months after he starts his job. Peter finds a job as a photographer for a local newspaper, and his first day of work is July 1, 2004. For tax reasons, Peter needs to compute the total amount of interest that he will pay to Aunt May in the year 2007. How much in interest did Peter actually pay in 2007? Answer=$[ANS].", "answer_v1": [ "2263.22" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Starting on July 1, 2000, Peter borrows $\\\\$8{,}900.00$ each year for 4 years from his dear Aunt May to pay for college. (Note: the last date that he borrows money is July 1, 2003.) From the beginning, Aunt May agreed to defer all interest on the loans until Peter finds a job; i.e. Peter's loans will not accumulate any interest until the first day he starts working. After that, Peter will be charged 7 percent compounded semiannually, and he will pay Aunt May back with 10 equal semiannual payments, the first coming 6 months after he starts his job. Peter finds a job as a photographer for a local newspaper, and his first day of work is July 1, 2004. For tax reasons, Peter needs to compute the total amount of interest that he will pay to Aunt May in the year 2007. How much in interest did Peter actually pay in 2007? Answer=$[ANS].", "answer_v2": [ "1474.78" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Starting on July 1, 2000, Peter borrows $\\\\$8{,}200.00$ each year for 4 years from his dear Aunt May to pay for college. (Note: the last date that he borrows money is July 1, 2003.) From the beginning, Aunt May agreed to defer all interest on the loans until Peter finds a job; i.e. Peter's loans will not accumulate any interest until the first day he starts working. After that, Peter will be charged 7.6 percent compounded semiannually, and he will pay Aunt May back with 12 equal semiannual payments, the first coming 6 months after he starts his job. Peter finds a job as a photographer for a local newspaper, and his first day of work is July 1, 2004. For tax reasons, Peter needs to compute the total amount of interest that he will pay to Aunt May in the year 2007. How much in interest did Peter actually pay in 2007? Answer=$[ANS].", "answer_v3": [ "1684.90" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0069", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Loans", "level": "4", "keywords": [], "problem_v1": "Suppose you take out a mortgage for \\$650000 at 6\\% interest per year compounded annually. If your mortgage is amortized over 25 years, what is your monthly mortgage payment? How much interest will you pay the lender by the end of the mortgage? What is the monthly interest rate corresponding to the effective annual rate? $r_m=$ [ANS]\nWhat are the monthly payments? [ANS]\nWhat is the total interest paid? [ANS]\n(you will lose 25\\% of your points if you do)", "answer_v1": [ "0.49", "4125.04", "587511" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": " Suppose you take out a mortgage for \\$250000 at 7.5\\% interest per year compounded bi-weekly. If your mortgage is amortized over 15 years, what is your monthly mortgage payment? How much interest will you pay the lender by the end of the mortgage? What is the monthly interest rate corresponding to the effective annual rate? $r_m=$ [ANS]\nWhat are the monthly payments? [ANS]\nWhat is the total interest paid? [ANS]\n(you will lose 25\\% of your points if you do)", "answer_v2": [ "0.63", "2319.2", "167455" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": " Suppose you take out a mortgage for \\$400000 at 6\\% interest per year compounded monthly. If your mortgage is amortized over 20 years, what is your monthly mortgage payment? How much interest will you pay the lender by the end of the mortgage? What is the monthly interest rate corresponding to the effective annual rate? $r_m=$ [ANS]\nWhat are the monthly payments? [ANS]\nWhat is the total interest paid? [ANS]\n(you will lose 25\\% of your points if you do)", "answer_v3": [ "0.5", "2865.72", "287774" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Financial_mathematics_0070", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Perpetuities", "level": "", "keywords": [ "financial mathematics", "perpetuities" ], "problem_v1": "A perpetuity will make annual payments, the first 8 years from now, following the sequence 1400, 1550, 1700,... If the effective rate of interest is 8.5 percent, what is the present value? Answer=[ANS] dollars", "answer_v1": [ "21033.2440633725" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A perpetuity will make annual payments, the first 5 years from now, following the sequence 1000, 1200, 1400,... If the effective rate of interest is 7.7 percent, what is the present value? Answer=[ANS] dollars", "answer_v2": [ "34724.4603820228" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A perpetuity will make annual payments, the first 6 years from now, following the sequence 1100, 1250, 1400,... If the effective rate of interest is 8.1 percent, what is the present value? Answer=[ANS] dollars", "answer_v3": [ "24687.7248585967" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0071", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Perpetuities", "level": "", "keywords": [ "financial mathematics", "perpetuities" ], "problem_v1": "Pam's fairy-godmother agrees to buy her a perpetuity that will make annual payments. The first payment will be 730 dollars and will come one year from now, and the payments will increase by 21 dollars every year after that. If Pam's fairy-godmother gets an effective interest rate of 6 percent, what will be the price of the perpetuity? Answer=[ANS] dollars.", "answer_v1": [ "18000" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Pam's fairy-godmother agrees to buy her a perpetuity that will make annual payments. The first payment will be 880 dollars and will come one year from now, and the payments will increase by 8 dollars every year after that. If Pam's fairy-godmother gets an effective interest rate of 4.9 percent, what will be the price of the perpetuity? Answer=[ANS] dollars.", "answer_v2": [ "21291.1286963765" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Pam's fairy-godmother agrees to buy her a perpetuity that will make annual payments. The first payment will be 740 dollars and will come one year from now, and the payments will increase by 12 dollars every year after that. If Pam's fairy-godmother gets an effective interest rate of 5.3 percent, what will be the price of the perpetuity? Answer=[ANS] dollars.", "answer_v3": [ "18234.2470630117" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0072", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Perpetuities", "level": "", "keywords": [ "financial mathematics", "perpetuities" ], "problem_v1": "Suppose that a perpetuity that pays 3400 dollars per year, starting one year from now, has a present value of 30000 dollars. Find the effective rate of interest. Answer=[ANS] percent.", "answer_v1": [ "11.3333333333333" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose that a perpetuity that pays 1800 dollars per year, starting one year from now, has a present value of 40000 dollars. Find the effective rate of interest. Answer=[ANS] percent.", "answer_v2": [ "4.5" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose that a perpetuity that pays 2400 dollars per year, starting one year from now, has a present value of 30000 dollars. Find the effective rate of interest. Answer=[ANS] percent.", "answer_v3": [ "8" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0073", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Perpetuities", "level": "", "keywords": [ "financial mathematics", "perpetuities" ], "problem_v1": "Pigpen wants to buy a perpetuity that will pay him 18500 dollars every three years, starting six years from now. If the perpetuity earns 6.5 percent effective, what is the present value of the perpetuity now? Answer=[ANS] dollars.", "answer_v1": [ "73648.6454272526" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Pigpen wants to buy a perpetuity that will pay him 17100 dollars every three years, starting six years from now. If the perpetuity earns 7.4 percent effective, what is the present value of the perpetuity now? Answer=[ANS] dollars.", "answer_v2": [ "57794.7680497904" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Pigpen wants to buy a perpetuity that will pay him 17600 dollars every three years, starting six years from now. If the perpetuity earns 6.6 percent effective, what is the present value of the perpetuity now? Answer=[ANS] dollars.", "answer_v3": [ "68742.845993938" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0074", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Perpetuities", "level": "", "keywords": [ "financial mathematics", "perpetuities" ], "problem_v1": "Find the present value of a perpetuity that pays 5650 dollars every year, starting 14 years from now. Assume a nominal rate of interest of 8.3 percent convertible quarterly. Answer=[ANS] dollars.", "answer_v1": [ "22681.3334224308" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Find the present value of a perpetuity that pays 4700 dollars every year, starting 11 years from now. Assume a nominal rate of interest of 9.3 percent convertible quarterly. Answer=[ANS] dollars.", "answer_v2": [ "19463.8509668299" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Find the present value of a perpetuity that pays 5050 dollars every year, starting 12 years from now. Assume a nominal rate of interest of 8.3 percent convertible quarterly. Answer=[ANS] dollars.", "answer_v3": [ "23892.7765744565" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0075", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Perpetuities", "level": "", "keywords": [ "financial mathematics", "perpetuities" ], "problem_v1": "Lucy has just purchased a perpetuity that will make annual payments, the first coming one year from now, that will increase by 85 dollars each year. If the perpetuity earns 7.8 percent effective, and Lucy paid 36000 dollars for the perpetuity, how large is the 10th payment? Answer=[ANS] dollars.", "answer_v1": [ "2483.25641025641" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Lucy has just purchased a perpetuity that will make annual payments, the first coming one year from now, that will increase by 35 dollars each year. If the perpetuity earns 6.3 percent effective, and Lucy paid 39500 dollars for the perpetuity, how large is the 10th payment? Answer=[ANS] dollars.", "answer_v2": [ "2247.94444444444" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Lucy has just purchased a perpetuity that will make annual payments, the first coming one year from now, that will increase by 50 dollars each year. If the perpetuity earns 6.9 percent effective, and Lucy paid 36000 dollars for the perpetuity, how large is the 10th payment? Answer=[ANS] dollars.", "answer_v3": [ "2209.36231884058" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0076", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Perpetuities", "level": "", "keywords": [ "financial mathematics", "perpetuities" ], "problem_v1": "Jeff would like to retire exactly 27 years from now. He is planning on saving up money to buy a perpetuity on the day he retires. He would like the perpetuity to pay him annual payments, with the first payment coming one year after he retires. He would like the first payment to be 32000 dollars, and then each payment thereafter will increase by 600 dollars. In order to save up money, Jeff will make annual deposits, starting a year from now, with the last coming on the day he retires. His deposits will increase by 1.6 percent each year. If both the perpetuity and his savings account earn 4.4 percent effective, how large will his first deposit be?\nAnswer=[ANS] dollars.", "answer_v1": [ "17461.312504998" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Jeff would like to retire exactly 20 years from now. He is planning on saving up money to buy a perpetuity on the day he retires. He would like the perpetuity to pay him annual payments, with the first payment coming one year after he retires. He would like the first payment to be 39000 dollars, and then each payment thereafter will increase by 300 dollars. In order to save up money, Jeff will make annual deposits, starting a year from now, with the last coming on the day he retires. His deposits will increase by 2.7 percent each year. If both the perpetuity and his savings account earn 3.6 percent effective, how large will his first deposit be?\nAnswer=[ANS] dollars.", "answer_v2": [ "36429.077822162" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Jeff would like to retire exactly 23 years from now. He is planning on saving up money to buy a perpetuity on the day he retires. He would like the perpetuity to pay him annual payments, with the first payment coming one year after he retires. He would like the first payment to be 32000 dollars, and then each payment thereafter will increase by 400 dollars. In order to save up money, Jeff will make annual deposits, starting a year from now, with the last coming on the day he retires. His deposits will increase by 1.4 percent each year. If both the perpetuity and his savings account earn 4 percent effective, how large will his first deposit be?\nAnswer=[ANS] dollars.", "answer_v3": [ "25094.013813263" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0077", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Perpetuities", "level": "", "keywords": [], "problem_v1": "Perpetuity A pays \\$ 100 at the end of each year. Perpetuity B pays \\$ 32 at the end of each quarter. The present value of Perpetuity A at the effective rate of interest $i$ is \\$ 833.33. What is the present value of Perpetuity B at the same annual effective rate of interest $i$?\nPresent value of Perpetuity B=[ANS]", "answer_v1": [ "1113.53363748367" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Perpetuity A pays \\$ 100 at the end of each year. Perpetuity B pays \\$ 39 at the end of each quarter. The present value of Perpetuity A at the effective rate of interest $i$ is \\$ 3333.33. What is the present value of Perpetuity B at the same annual effective rate of interest $i$?\nPresent value of Perpetuity B=[ANS]", "answer_v2": [ "5258.13975767144" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Perpetuity A pays \\$ 100 at the end of each year. Perpetuity B pays \\$ 32 at the end of each quarter. The present value of Perpetuity A at the effective rate of interest $i$ is \\$ 1666.67. What is the present value of Perpetuity B at the same annual effective rate of interest $i$?\nPresent value of Perpetuity B=[ANS]", "answer_v3": [ "2180.75067928314" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0078", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Perpetuities", "level": "", "keywords": [], "problem_v1": "Betty received \\$ 500,000 from a life insurance policy to be distributed to her as an annuity certain in 10 equal annual installments with the first payment made immediately. On the day she receives her third payment, she is offered a monthly perpetuity of X in lieu of the future annual payments. The first payment will be made in exactly one month. The effective annual rate of interest is 12 \\%. Determine the value of X.\nX=[ANS]", "answer_v1": [ "-5952.38095238095" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Betty received \\$ 500,000 from a life insurance policy to be distributed to her as an annuity certain in 10 equal annual installments with the first payment made immediately. On the day she receives her third payment, she is offered a monthly perpetuity of X in lieu of the future annual payments. The first payment will be made in exactly one month. The effective annual rate of interest is 3 \\%. Determine the value of X.\nX=[ANS]", "answer_v2": [ "-1618.12297734628" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Betty received \\$ 500,000 from a life insurance policy to be distributed to her as an annuity certain in 10 equal annual installments with the first payment made immediately. On the day she receives her third payment, she is offered a monthly perpetuity of X in lieu of the future annual payments. The first payment will be made in exactly one month. The effective annual rate of interest is 6 \\%. Determine the value of X.\nX=[ANS]", "answer_v3": [ "-3144.65408805031" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0079", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Perpetuities", "level": "3", "keywords": [ "financial mathematics", "compound interest" ], "problem_v1": "Most scholarships are established by making a one time deposit into an account. The scholarship money is then taken from the earned interest on the account at the end of each investment year. How much money should you deposit into an account earning an annual interest rate of $5.49 \\%$ compounded weekly to establish an annual scholarship worth $\\\\$1{,}300.00$? $[ANS]\n", "answer_v1": [ "23047.86" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Most scholarships are established by making a one time deposit into an account. The scholarship money is then taken from the earned interest on the account at the end of each investment year. How much money should you deposit into an account earning an annual interest rate of $7.591 \\%$ compounded continuously to establish an annual scholarship worth $\\\\$500.00$? $[ANS]\n", "answer_v2": [ "6339.91" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Most scholarships are established by making a one time deposit into an account. The scholarship money is then taken from the earned interest on the account at the end of each investment year. How much money should you deposit into an account earning an annual interest rate of $5.633 \\%$ compounded quarterly to establish an annual scholarship worth $\\\\$800.00$? $[ANS]\n", "answer_v3": [ "13,905.52" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0080", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "financial mathematics", "annuities" ], "problem_v1": "You open a savings account on June 1, 2000, and decide to make annual deposits of the form $330,510,330,510,\\ldots$, the first coming on June 1, 2001. You manage to keep this up-almost. Instead of making your regular deposit on June 1, 2013, you make a deposit of only 160 dollars on that day. You are able to make all the rest of the deposits as originally planned. (Note: your deposit on June 1, 2014 will be 510 dollars.) What is the balance in your account immediately after you make your deposit on June 1, 2033, assuming the account earns an effective rate of interest of 2.7 percent throughout?\nAnswer=[ANS] dollars.", "answer_v1": [ "21475.7303233165" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "You open a savings account on June 1, 2000, and decide to make annual deposits of the form $250,550,250,550,\\ldots$, the first coming on June 1, 2001. You manage to keep this up-almost. Instead of making your regular deposit on June 1, 2013, you make a deposit of only 110 dollars on that day. You are able to make all the rest of the deposits as originally planned. (Note: your deposit on June 1, 2014 will be 550 dollars.) What is the balance in your account immediately after you make your deposit on June 1, 2033, assuming the account earns an effective rate of interest of 2.3 percent throughout?\nAnswer=[ANS] dollars.", "answer_v2": [ "18989.1319043326" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "You open a savings account on June 1, 2000, and decide to make annual deposits of the form $280,510,280,510,\\ldots$, the first coming on June 1, 2001. You manage to keep this up-almost. Instead of making your regular deposit on June 1, 2013, you make a deposit of only 130 dollars on that day. You are able to make all the rest of the deposits as originally planned. (Note: your deposit on June 1, 2014 will be 510 dollars.) What is the balance in your account immediately after you make your deposit on June 1, 2033, assuming the account earns an effective rate of interest of 2.6 percent throughout?\nAnswer=[ANS] dollars.", "answer_v3": [ "19807.3108149769" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0081", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "financial mathematics", "annuities" ], "problem_v1": "Kimberly has just started her first job and decides to begin saving for a car. She opens a savings account on October 1, 2003 with a deposit of 180 dollars, and will continue to make deposits of the same amount at the beginning of each month until October 1, 2007, when she will make the final deposit. If the account pays a nominal rate of interest of 11.4 percent convertible monthly, how much is in the account on October 1, 2011, (when Kimberly will use this money as a down payment for a car)?\nAnswer=[ANS] dollars.", "answer_v1": [ "17579.2171489629" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Kimberly has just started her first job and decides to begin saving for a car. She opens a savings account on October 1, 2003 with a deposit of 100 dollars, and will continue to make deposits of the same amount at the beginning of each month until October 1, 2006, when she will make the final deposit. If the account pays a nominal rate of interest of 12.6 percent convertible monthly, how much is in the account on October 1, 2010, (when Kimberly will use this money as a down payment for a car)?\nAnswer=[ANS] dollars.", "answer_v2": [ "7418.15968152949" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Kimberly has just started her first job and decides to begin saving for a car. She opens a savings account on October 1, 2003 with a deposit of 130 dollars, and will continue to make deposits of the same amount at the beginning of each month until October 1, 2006, when she will make the final deposit. If the account pays a nominal rate of interest of 11.4 percent convertible monthly, how much is in the account on October 1, 2010, (when Kimberly will use this money as a down payment for a car)?\nAnswer=[ANS] dollars.", "answer_v3": [ "9023.46289705333" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0082", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "financial mathematics", "annuities" ], "problem_v1": "Anuual deposits of 160 dollars each are placed into an account paying a nominal rate of 7.8 percent convertible monthly, starting on October 1, 2003. How much is in the account immediately after the deposit on October 1, 2034? Answer=[ANS] dollars.", "answer_v1": [ "21840.4977334923" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Anuual deposits of 120 dollars each are placed into an account paying a nominal rate of 9 percent convertible monthly, starting on October 1, 2001. How much is in the account immediately after the deposit on October 1, 2030? Answer=[ANS] dollars.", "answer_v2": [ "17564.4774070223" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Anuual deposits of 135 dollars each are placed into an account paying a nominal rate of 7.8 percent convertible monthly, starting on October 1, 2002. How much is in the account immediately after the deposit on October 1, 2032? Answer=[ANS] dollars.", "answer_v3": [ "16924.571561379" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0083", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "financial mathematics", "annuities" ], "problem_v1": "Grandma Dayhoff has set up a trust fund for her grandson Donny that will make annual payments of 41000 dollars for 18 years, starting on his 30th birthday. Today is Donny's 21st birthday, and he meets with a tax expert and learns that the IRS will charge him a tax of 16 percent of the present value of all the trust fund payments on the day he receives the first payment. (The tax is due on the day he receives the first payment.) To budget for the anticipated tax bill, Donny will make annual savings account deposits of $X$ dollars, the first today and the last coming on his 30th birthday. If his goal is to have exactly enough in the savings account to pay the tax bill, and we assume an effective rate of 8.3 percent throughout, how large should Donny's annual deposits be? Answer=[ANS] dollars.", "answer_v1": [ "4438.30665114554" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Grandma Dayhoff has set up a trust fund for her grandson Donny that will make annual payments of 28000 dollars for 20 years, starting on his 30th birthday. Today is Donny's 21st birthday, and he meets with a tax expert and learns that the IRS will charge him a tax of 14 percent of the present value of all the trust fund payments on the day he receives the first payment. (The tax is due on the day he receives the first payment.) To budget for the anticipated tax bill, Donny will make annual savings account deposits of $X$ dollars, the first today and the last coming on his 30th birthday. If his goal is to have exactly enough in the savings account to pay the tax bill, and we assume an effective rate of 6.2 percent throughout, how large should Donny's annual deposits be? Answer=[ANS] dollars.", "answer_v2": [ "3531.24024731127" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Grandma Dayhoff has set up a trust fund for her grandson Donny that will make annual payments of 32000 dollars for 18 years, starting on his 30th birthday. Today is Donny's 21st birthday, and he meets with a tax expert and learns that the IRS will charge him a tax of 15 percent of the present value of all the trust fund payments on the day he receives the first payment. (The tax is due on the day he receives the first payment.) To budget for the anticipated tax bill, Donny will make annual savings account deposits of $X$ dollars, the first today and the last coming on his 30th birthday. If his goal is to have exactly enough in the savings account to pay the tax bill, and we assume an effective rate of 6.9 percent throughout, how large should Donny's annual deposits be? Answer=[ANS] dollars.", "answer_v3": [ "3780.70216638155" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0084", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "financial mathematics", "annuities" ], "problem_v1": "Janelle makes monthly deposits of 130 dollars into an account that pays an effective rate of interest of 7.3 percent. How much will she have in the account immediately after the 28th deposit?\nAnswer=[ANS] dollars.", "answer_v1": [ "3944.70410127168" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Janelle makes monthly deposits of 50 dollars into an account that pays an effective rate of interest of 8.8 percent. How much will she have in the account immediately after the 26th deposit?\nAnswer=[ANS] dollars.", "answer_v2": [ "1421.35207216624" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Janelle makes monthly deposits of 80 dollars into an account that pays an effective rate of interest of 7.4 percent. How much will she have in the account immediately after the 27th deposit?\nAnswer=[ANS] dollars.", "answer_v3": [ "2336.18843645468" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0085", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "financial mathematics", "varying payments" ], "problem_v1": "David is a professional rodeo competitor who would like to have 860000 dollars saved up for when he begins retirement 41 years from now. To reach his goal, he plans to make a sequence of 15 annual deposits, starting with an immediate deposit, and increasing the deposit size by 4.5 percent per year. If the account pays an effective rate of interest of 8 percent, how large should his first deposit be?\nAnswer=[ANS] dollars.", "answer_v1": [ "3046.4579496928" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "David is a professional rodeo competitor who would like to have 700000 dollars saved up for when he begins retirement 39 years from now. To reach his goal, he plans to make a sequence of 17 annual deposits, starting with an immediate deposit, and increasing the deposit size by 3.8 percent per year. If the account pays an effective rate of interest of 8.8 percent, how large should his first deposit be?\nAnswer=[ANS] dollars.", "answer_v2": [ "2178.21677575445" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "David is a professional rodeo competitor who would like to have 760000 dollars saved up for when he begins retirement 40 years from now. To reach his goal, he plans to make a sequence of 14 annual deposits, starting with an immediate deposit, and increasing the deposit size by 4 percent per year. If the account pays an effective rate of interest of 8 percent, how large should his first deposit be?\nAnswer=[ANS] dollars.", "answer_v3": [ "3156.88515374446" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0086", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "financial mathematics", "varying payments" ], "problem_v1": "Walter makes a sequence of annual deposits into an account paying an effective rate of interest of 8.7 percent. The first deposit of 700 dollars comes one year from now, and each subsequent deposit is 125 dollars larger than the last. If he will make 17 such deposits, what is their present value now? Answer=[ANS] dollars.", "answer_v1": [ "12698.3866928066" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Walter makes a sequence of annual deposits into an account paying an effective rate of interest of 7 percent. The first deposit of 900 dollars comes one year from now, and each subsequent deposit is 50 dollars larger than the last. If he will make 14 such deposits, what is their present value now? Answer=[ANS] dollars.", "answer_v2": [ "10239.5116235089" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Walter makes a sequence of annual deposits into an account paying an effective rate of interest of 7.6 percent. The first deposit of 800 dollars comes one year from now, and each subsequent deposit is 75 dollars larger than the last. If he will make 16 such deposits, what is their present value now? Answer=[ANS] dollars.", "answer_v3": [ "11337.9483321871" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0087", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "financial mathematics", "varying payments" ], "problem_v1": "Sandra makes a sequence of 29 annual deposits into an account paying an effective rate of 9 percent. The deposits increase by a fixed percentage from one to the next, and the last deposit is 3 times as large as the first. If the account balance is 411000 dollars immediately after the last deposit is made, how large is the last deposit?\nAnswer=[ANS] dollars.", "answer_v1": [ "6808.36158984061" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Sandra makes a sequence of 34 annual deposits into an account paying an effective rate of 7.6 percent. The deposits increase by a fixed percentage from one to the next, and the last deposit is 2 times as large as the first. If the account balance is 301000 dollars immediately after the last deposit is made, how large is the last deposit?\nAnswer=[ANS] dollars.", "answer_v2": [ "3289.1208605141" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Sandra makes a sequence of 30 annual deposits into an account paying an effective rate of 8.1 percent. The deposits increase by a fixed percentage from one to the next, and the last deposit is 2 times as large as the first. If the account balance is 361000 dollars immediately after the last deposit is made, how large is the last deposit?\nAnswer=[ANS] dollars.", "answer_v3": [ "4943.26422549019" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0088", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "financial mathematics", "varying payments" ], "problem_v1": "The Little Red-Haired Girl makes quarterly deposits into an account paying an interest rate of 3.5 percent per quarter. The first deposit is 4600 dollars, and each subsequent deposit is 150 dollars SMALLER than the previous one. How much is in the account immediately after the 15th deposit? Answer=[ANS] dollars.", "answer_v1": [ "70350.0711332847" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "The Little Red-Haired Girl makes quarterly deposits into an account paying an interest rate of 2.1 percent per quarter. The first deposit is 4950 dollars, and each subsequent deposit is 75 dollars SMALLER than the previous one. How much is in the account immediately after the 12th deposit? Answer=[ANS] dollars.", "answer_v2": [ "61450.9862773727" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "The Little Red-Haired Girl makes quarterly deposits into an account paying an interest rate of 2.6 percent per quarter. The first deposit is 4600 dollars, and each subsequent deposit is 75 dollars SMALLER than the previous one. How much is in the account immediately after the 14th deposit? Answer=[ANS] dollars.", "answer_v3": [ "68912.5065618612" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0089", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "financial mathematics", "varying payments" ], "problem_v1": "Sue opens a retirement account with a deposit of 1700 dollars. Each year, she makes another deposit that is 4.5 percent larger than the one from the previous year. If the account pays an effective rate of interest of 8 percent, what will be the amount of her 39th deposit?\nAnswer=[ANS] dollars.", "answer_v1": [ "9054.57266446798" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Sue opens a retirement account with a deposit of 1420 dollars. Each year, she makes another deposit that is 3.8 percent larger than the one from the previous year. If the account pays an effective rate of interest of 8.8 percent, what will be the amount of her 36th deposit?\nAnswer=[ANS] dollars.", "answer_v2": [ "5238.36453325986" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Sue opens a retirement account with a deposit of 1520 dollars. Each year, she makes another deposit that is 4 percent larger than the one from the previous year. If the account pays an effective rate of interest of 8 percent, what will be the amount of her 37th deposit?\nAnswer=[ANS] dollars.", "answer_v3": [ "6237.97748205024" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0090", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "financial mathematics", "geometric sums" ], "problem_v1": "On April 15, 1976, Walter opens an account with a deposit of 33000 dollars. The account pays a nominal rate of interest of 8.9 percent convertible quarterly. Starting on April 15, 1977, he makes yearly deposits of 4000 dollars until April 15, 1993, when he makes the final deposit of 4000 dollars. How much is in the account on April 15, 1996?\nAnswer=[ANS] dollars.", "answer_v1": [ "388091.67582031" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "On April 15, 1976, Walter opens an account with a deposit of 25000 dollars. The account pays a nominal rate of interest of 7.5 percent convertible quarterly. Starting on April 15, 1977, he makes yearly deposits of 4550 dollars until April 15, 1993, when he makes the final deposit of 4550 dollars. How much is in the account on April 15, 1996?\nAnswer=[ANS] dollars.", "answer_v2": [ "297494.263157487" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "On April 15, 1976, Walter opens an account with a deposit of 28000 dollars. The account pays a nominal rate of interest of 7.9 percent convertible quarterly. Starting on April 15, 1977, he makes yearly deposits of 4050 dollars until April 15, 1993, when he makes the final deposit of 4050 dollars. How much is in the account on April 15, 1996?\nAnswer=[ANS] dollars.", "answer_v3": [ "308871.269354417" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0091", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "financial mathematics", "geometric sums" ], "problem_v1": "Bill invests 145 dollars per year on the first day of the year, with the first deposit coming on January 1, 1950. The account pays 6.3 percent effective interest. Just prior to making his January 1, 1960 deposit, Bill learns that he can begin to get 6.6 percent effective interest on his money if he increases his deposits to 200 dollars. He does so, making the first deposit of 200 dollars on January 1, 1960, and the final deposit on January 1, 1980. How much is in the account immediately after he makes the final deposit?\nAnswer=[ANS] dollars.", "answer_v1": [ "15965.7540494253" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Bill invests 120 dollars per year on the first day of the year, with the first deposit coming on January 1, 1950. The account pays 5.3 percent effective interest. Just prior to making his January 1, 1960 deposit, Bill learns that he can begin to get 5.5 percent effective interest on his money if he increases his deposits to 210 dollars. He does so, making the first deposit of 210 dollars on January 1, 1960, and the final deposit on January 1, 1980. How much is in the account immediately after he makes the final deposit?\nAnswer=[ANS] dollars.", "answer_v2": [ "12637.8452038961" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Bill invests 130 dollars per year on the first day of the year, with the first deposit coming on January 1, 1950. The account pays 5.6 percent effective interest. Just prior to making his January 1, 1960 deposit, Bill learns that he can begin to get 5.9 percent effective interest on his money if he increases his deposits to 200 dollars. He does so, making the first deposit of 200 dollars on January 1, 1960, and the final deposit on January 1, 1980. How much is in the account immediately after he makes the final deposit?\nAnswer=[ANS] dollars.", "answer_v3": [ "13496.7644845467" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0092", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "financial mathematics", "geometric sums" ], "problem_v1": "Bubba makes annual deposits of 2300 dollars into an account, with the first coming on August 1, 1980, and the last on August 1, 1988. On August 1, 1990, he makes a deposit of 4000 dollars, and continues to do so once each year until making a final deposit on August 1, 2000. If the account pays an effective rate of interest of 8.9 percent, how much is in the account on August 1, 2005?\nAnswer=[ANS] dollars.", "answer_v1": [ "234069.743796154" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Bubba makes annual deposits of 1500 dollars into an account, with the first coming on August 1, 1980, and the last on August 1, 1988. On August 1, 1990, he makes a deposit of 4550 dollars, and continues to do so once each year until making a final deposit on August 1, 2000. If the account pays an effective rate of interest of 7.5 percent, how much is in the account on August 1, 2005?\nAnswer=[ANS] dollars.", "answer_v2": [ "168600.521094523" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Bubba makes annual deposits of 1750 dollars into an account, with the first coming on August 1, 1980, and the last on August 1, 1988. On August 1, 1990, he makes a deposit of 4050 dollars, and continues to do so once each year until making a final deposit on August 1, 2000. If the account pays an effective rate of interest of 7.9 percent, how much is in the account on August 1, 2005?\nAnswer=[ANS] dollars.", "answer_v3": [ "177333.973045767" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0093", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "financial mathematics", "geometric sums" ], "problem_v1": "Irene plans to retire on January 1, 2020. She has been preparing to retire by making annual deposits, starting on January 1, 1980, of 2400 dollars into an account that pays an effective rate of interest of 8.9 percent. She has continued this practice every year through January 1, 2001. Her goal is to have 1.4 million dollars saved up at the time of her retirement. How large should her annual deposits be (from January 1, 2002 until January 1, 2020) so that she can reach her goal?\nAnswer=[ANS] dollars.", "answer_v1": [ "14211.0771694454" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Irene plans to retire on January 1, 2020. She has been preparing to retire by making annual deposits, starting on January 1, 1980, of 2000 dollars into an account that pays an effective rate of interest of 7.5 percent. She has continued this practice every year through January 1, 2001. Her goal is to have 1.5 million dollars saved up at the time of her retirement. How large should her annual deposits be (from January 1, 2002 until January 1, 2020) so that she can reach her goal?\nAnswer=[ANS] dollars.", "answer_v2": [ "27649.7232646406" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Irene plans to retire on January 1, 2020. She has been preparing to retire by making annual deposits, starting on January 1, 1980, of 2150 dollars into an account that pays an effective rate of interest of 7.9 percent. She has continued this practice every year through January 1, 2001. Her goal is to have 1.4 million dollars saved up at the time of her retirement. How large should her annual deposits be (from January 1, 2002 until January 1, 2020) so that she can reach her goal?\nAnswer=[ANS] dollars.", "answer_v3": [ "21957.8993370629" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0094", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "financial mathematics", "geometric sums" ], "problem_v1": "Barbara makes a sequence of 26 semiannual deposits of the form $X,2X,X,2X,\\ldots$ into an account paying a nominal rate of 7.8 percent convertible quarterly. If the account balance 8 years after the last deposit is 11000, what is $X$?\nAnswer=[ANS] dollars.", "answer_v1": [ "90.5709584826009" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Barbara makes a sequence of 30 semiannual deposits of the form $X,2X,X,2X,\\ldots$ into an account paying a nominal rate of 6.6 percent convertible quarterly. If the account balance 6 years after the last deposit is 8300, what is $X$?\nAnswer=[ANS] dollars.", "answer_v2": [ "74.8617401385813" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Barbara makes a sequence of 26 semiannual deposits of the form $X,2X,X,2X,\\ldots$ into an account paying a nominal rate of 6.8 percent convertible quarterly. If the account balance 7 years after the last deposit is 9250, what is $X$?\nAnswer=[ANS] dollars.", "answer_v3": [ "94.5622733973005" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0095", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "financial mathematics", "geometric sums" ], "problem_v1": "Hannibal opens a savings account on January 1, 1984 with a deposit of 330 dollars, and continues to make deposits of the same amount at the beginning of each month until January 1, 1990, when he makes the final deposit. If the account pays a nominal rate of interest of 5.7 percent convertible monthly, how much is in the account on January 1, 1998?\nAnswer=[ANS] dollars.", "answer_v1": [ "45254.0701238352" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Hannibal opens a savings account on January 1, 1984 with a deposit of 250 dollars, and continues to make deposits of the same amount at the beginning of each month until January 1, 1990, when he makes the final deposit. If the account pays a nominal rate of interest of 6.7 percent convertible monthly, how much is in the account on January 1, 1998?\nAnswer=[ANS] dollars.", "answer_v2": [ "38320.6109130356" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Hannibal opens a savings account on January 1, 1984 with a deposit of 280 dollars, and continues to make deposits of the same amount at the beginning of each month until January 1, 1990, when he makes the final deposit. If the account pays a nominal rate of interest of 5.9 percent convertible monthly, how much is in the account on January 1, 1998?\nAnswer=[ANS] dollars.", "answer_v3": [ "39261.2527593569" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0096", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "financial mathematics", "geometric sums" ], "problem_v1": "David makes a sequence of 37 monthly deposits of 595 dollars each into an account paying interest convertible monthly. Immediately after making the 37th deposit, the account balance is 24454.17 dollars. What is the nominal rate of interest convertible monthly?\nAnswer=[ANS] percent.", "answer_v1": [ "6.9" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "David makes a sequence of 39 monthly deposits of 435 dollars each into an account paying interest convertible monthly. Immediately after making the 39th deposit, the account balance is 18529.44 dollars. What is the nominal rate of interest convertible monthly?\nAnswer=[ANS] percent.", "answer_v2": [ "5.5" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "David makes a sequence of 37 monthly deposits of 490 dollars each into an account paying interest convertible monthly. Immediately after making the 37th deposit, the account balance is 19830.52 dollars. What is the nominal rate of interest convertible monthly?\nAnswer=[ANS] percent.", "answer_v3": [ "5.9" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0097", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "financial mathematics", "geometric sums" ], "problem_v1": "Theodore invests 5440 dollars on a yearly basis at an effective rate of interest of 6.8 percent. He makes the first deposit on June 1, 1973, and the final deposit on June 1, 1995. How much is the investment worth on June 1, 2010?\nAnswer=[ANS] dollars.", "answer_v1": [ "759920.972365463" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Theodore invests 4120 dollars on a yearly basis at an effective rate of interest of 7.8 percent. He makes the first deposit on June 1, 1973, and the final deposit on June 1, 1995. How much is the investment worth on June 1, 2007?\nAnswer=[ANS] dollars.", "answer_v2": [ "601827.476331352" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Theodore invests 4600 dollars on a yearly basis at an effective rate of interest of 6.8 percent. He makes the first deposit on June 1, 1973, and the final deposit on June 1, 1995. How much is the investment worth on June 1, 2007?\nAnswer=[ANS] dollars.", "answer_v3": [ "527489.23900796" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0098", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "algebra", "geometric sequence" ], "problem_v1": "Steve and Amanda want to purchase a house. Suppose they invest $500$ dollars into a mutual fund at the end of each month. How much will they have for a downpayment after $8$ years if the per annum rate of return of the mutual fund is assumed to be $9.5$ percent compounded monthly? [ANS]", "answer_v1": [ "71487.5929015274" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Daniel and Alice want to purchase a house. Suppose they invest $300$ dollars into a mutual fund at the end of each month. How much will they have for a downpayment after $5$ years if the per annum rate of return of the mutual fund is assumed to be $11$ percent compounded monthly? [ANS]", "answer_v2": [ "23855.4239057484" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Alex and Amanda want to purchase a house. Suppose they invest $400$ dollars into a mutual fund at the end of each month. How much will they have for a downpayment after $7$ years if the per annum rate of return of the mutual fund is assumed to be $9.5$ percent compounded monthly? [ANS]", "answer_v3": [ "47464.7024948636" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0099", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "A company establishes a sinking fund to pay off a debt of \\$180000 due in 9 years. Find the amount of the annual deposits if interest is 11\\% per annum. Answer=\\$ [ANS]", "answer_v1": [ "12708.2995852595" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A company establishes a sinking fund to pay off a debt of \\$100000 due in 12 years. Find the amount of the annual deposits if interest is 5\\% per annum. Answer=\\$ [ANS]", "answer_v2": [ "6282.54100208153" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A company establishes a sinking fund to pay off a debt of \\$130000 due in 9 years. Find the amount of the annual deposits if interest is 7\\% per annum. Answer=\\$ [ANS]", "answer_v3": [ "10853.2411179948" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0100", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "percent", "mathematics for business", "annuity" ], "problem_v1": "Hal invested \\$1800 per year in an IRA each year for 8 years earning 12\\% compounded annually. At the end of 8 years he ceased the IRA payments, but continued to invest his accumulated amount at 12\\% compounded annually for the next 6 years. a) What was the value of his IRA at the end of 8 years? Answer=\\$ [ANS]\nb) What was the value of the investment at the end of the next 6 years? Answer=\\$ [ANS]", "answer_v1": [ "22139.4476444222", "43699.343998004" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Hal invested \\$1000 per year in an IRA each year for 10 years earning 7\\% compounded annually. At the end of 10 years he ceased the IRA payments, but continued to invest his accumulated amount at 7\\% compounded annually for the next 3 years. a) What was the value of his IRA at the end of 10 years? Answer=\\$ [ANS]\nb) What was the value of the investment at the end of the next 3 years? Answer=\\$ [ANS]", "answer_v2": [ "13816.4479612795", "16925.7428598297" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Hal invested \\$1300 per year in an IRA each year for 8 years earning 10\\% compounded annually. At the end of 8 years he ceased the IRA payments, but continued to invest his accumulated amount at 10\\% compounded annually for the next 4 years. a) What was the value of his IRA at the end of 8 years? Answer=\\$ [ANS]\nb) What was the value of the investment at the end of the next 4 years? Answer=\\$ [ANS]", "answer_v3": [ "14866.65453", "21766.268897373" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0101", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "In 6 years Harry and Sally would like to have \\$26000 for a down payment on a house. How much should they deposit each month into an account paying 11\\% compounded monthly? Answer=\\$ [ANS]", "answer_v1": [ "256.552720685014" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "In 8 years Harry and Sally would like to have \\$10000 for a down payment on a house. How much should they deposit each month into an account paying 5\\% compounded monthly? Answer=\\$ [ANS]", "answer_v2": [ "84.9325334545716" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "In 6 years Harry and Sally would like to have \\$16000 for a down payment on a house. How much should they deposit each month into an account paying 7\\% compounded monthly? Answer=\\$ [ANS]", "answer_v3": [ "179.45077021818" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0102", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "Mr. Smith wants to save for his son's college education. If he deposits \\$700 each month at 11\\% compounded monthly, how much will he have in the account after 12 years? Answer=\\$ [ANS]", "answer_v1": [ "207783.826524611" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Mr. Smith wants to save for his son's college education. If he deposits \\$200 each month at 4\\% compounded monthly, how much will he have in the account after 15 years? Answer=\\$ [ANS]", "answer_v2": [ "49218.0976422177" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Mr. Smith wants to save for his son's college education. If he deposits \\$400 each month at 6\\% compounded monthly, how much will he have in the account after 12 years? Answer=\\$ [ANS]", "answer_v3": [ "84060.0652448521" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0103", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "Mark deposits \\$1300 each month in a retirement plan paying 11\\% compounded monthly. How much will he have in the account after 22 years? Answer=\\$ [ANS]", "answer_v1": [ "1435563.33054618" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Mark deposits \\$500 each month in a retirement plan paying 4\\% compounded monthly. How much will he have in the account after 30 years? Answer=\\$ [ANS]", "answer_v2": [ "347024.702191041" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Mark deposits \\$800 each month in a retirement plan paying 6\\% compounded monthly. How much will he have in the account after 22 years? Answer=\\$ [ANS]", "answer_v3": [ "436980.693783217" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0104", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "How many years will it take to save \\$160000 if you place \\$1800 per month in an account that earns 11\\% compounded monthly? Answer=[ANS] years", "answer_v1": [ "5.44282607809357" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "How many years will it take to save \\$200000 if you place \\$1000 per month in an account that earns 4\\% compounded monthly? Answer=[ANS] years", "answer_v2": [ "12.7919131901388" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "How many years will it take to save \\$160000 if you place \\$1300 per month in an account that earns 6\\% compounded monthly? Answer=[ANS] years", "answer_v3": [ "8.01285027236437" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0105", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "percent" ], "problem_v1": "a) How much must be placed each month into a retirement account earning 10\\% compounded monthly if the value of the account is to reach \\$ 1,000,000 in 30 years? Answer=\\$ [ANS]\nb) If the account continues to earn 10\\% after retirement, how much per year will the account earn? Answer=\\$ [ANS]", "answer_v1": [ "442.382367554659", "100000" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "a) How much must be placed each month into a retirement account earning 15\\% compounded monthly if the value of the account is to reach \\$ 1,000,000 in 15 years? Answer=\\$ [ANS]\nb) If the account continues to earn 15\\% after retirement, how much per year will the account earn? Answer=\\$ [ANS]", "answer_v2": [ "1495.87118744574", "150000" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "a) How much must be placed each month into a retirement account earning 10\\% compounded monthly if the value of the account is to reach \\$ 1,000,000 in 20 years? Answer=\\$ [ANS]\nb) If the account continues to earn 10\\% after retirement, how much per year will the account earn? Answer=\\$ [ANS]", "answer_v3": [ "1316.88311740676", "100000" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0106", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "percent" ], "problem_v1": "A silver mine is expected to yield a constant annual income for the next 22 years, after which it will be sold for \\$7150. An investor wants an annual return on his investment of 14\\%, so he pays \\$811354.22 for the mine. If he can establish a sinking fund earning an annual interest rate of 7\\%, to which he pays an annual payment that will accumulate to his total outlay for the mine, what is the constant annual income from the mine? Answer=\\$ [ANS]", "answer_v1": [ "130000" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A copper mine is expected to yield a constant annual income for the next 12 years, after which it will be sold for \\$4000. An investor wants an annual return on his investment of 8\\%, so he pays \\$342991.9 for the mine. If he can establish a sinking fund earning an annual interest rate of 4\\%, to which he pays an annual payment that will accumulate to his total outlay for the mine, what is the constant annual income from the mine? Answer=\\$ [ANS]", "answer_v2": [ "50000" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A silver mine is expected to yield a constant annual income for the next 16 years, after which it will be sold for \\$4400. An investor wants an annual return on his investment of 12\\%, so he pays \\$504374.38 for the mine. If he can establish a sinking fund earning an annual interest rate of 6\\%, to which he pays an annual payment that will accumulate to his total outlay for the mine, what is the constant annual income from the mine? Answer=\\$ [ANS]", "answer_v3": [ "80000" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0107", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "percent" ], "problem_v1": "In 9 years Ed and Trixie would like to have \\$26000 for a down payment on a house. Their budget only allows them to save \\$881.91 per half-year. What nominal annual interest rate, compounded semi-annually, must their saving account pay? Answer=[ANS] \\%.", "answer_v1": [ "11" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "In 12 years Nicholas and Natalie would like to have \\$10000 for a down payment on a house. Their budget only allows them to save \\$153.3 per quarter. What nominal annual interest rate, compounded quarterly, must their saving account pay? Answer=[ANS] \\%.", "answer_v2": [ "5" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "In 9 years Ed and Trixie would like to have \\$16000 for a down payment on a house. Their budget only allows them to save \\$653.06 per half-year. What nominal annual interest rate, compounded semi-annually, must their saving account pay? Answer=[ANS] \\%.", "answer_v3": [ "7" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0108", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [], "problem_v1": "At a certain interest rate, the present value of the following two payment patterns are equal: (i) \\$ 1600 at the end of five years, plus \\$ 2700 at the end of ten years, (ii) \\$ 2535 at the end of five years. At the same interest rate, \\$ 100 invested now, plus \\$ 120 invested at the end of five years will accumulate to P at the end of ten years. Calculate P. P=\\$ [ANS]", "answer_v1": [ "1180.41" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "At a certain interest rate, the present value of the following two payment patterns are equal: (i) \\$ 500 at the end of five years, plus \\$ 2900 at the end of ten years, (ii) \\$ 2540 at the end of five years. At the same interest rate, \\$ 100 invested now, plus \\$ 120 invested at the end of five years will accumulate to P at the end of ten years. Calculate P. P=\\$ [ANS]", "answer_v2": [ "372.67" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "At a certain interest rate, the present value of the following two payment patterns are equal: (i) \\$ 900 at the end of five years, plus \\$ 2500 at the end of ten years, (ii) \\$ 2260 at the end of five years. At the same interest rate, \\$ 100 invested now, plus \\$ 120 invested at the end of five years will accumulate to P at the end of ten years. Calculate P. P=\\$ [ANS]", "answer_v3": [ "558.5" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0109", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "1", "keywords": [], "problem_v1": "An annuity due has the following present value and accumulated value:\n$\\ddot a_{\\overline{n+2}\\rceil}=14.26$\n$\\ddot s_{n\\rceil}=50.33$\nDetermine the effective annual rate of interest $i$.\n$i$=[ANS] \\%", "answer_v1": [ "5.59329967656712" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "An annuity due has the following present value and accumulated value:\n$\\ddot a_{\\overline{n+2}\\rceil}=12.24$\n$\\ddot s_{n\\rceil}=51.73$\nDetermine the effective annual rate of interest $i$.\n$i$=[ANS] \\%", "answer_v2": [ "7.00034352131621" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "An annuity due has the following present value and accumulated value:\n$\\ddot a_{\\overline{n+2}\\rceil}=12.94$\n$\\ddot s_{n\\rceil}=50.42$\nDetermine the effective annual rate of interest $i$.\n$i$=[ANS] \\%", "answer_v3": [ "6.43044080769464" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0110", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "1", "keywords": [ "arithmetic progression", "unknown interest rate" ], "problem_v1": "If ${(Is)}_{3\\rceil}$=6.98, find and expression of the interest per period for i. i=[ANS] \\%?", "answer_v1": [ "23.159" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "If ${(Is)}_{3\\rceil}$=6.11, find and expression of the interest per period for i. i=[ANS] \\%?", "answer_v2": [ "2.731" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "If ${(Is)}_{3\\rceil}$=6.41, find and expression of the interest per period for i. i=[ANS] \\%?", "answer_v3": [ "10" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0111", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "5", "keywords": [ "accumulated amount" ], "problem_v1": "Hannah wishes to accumulate \\$ 140000 in a fund at the end of 25 years. She plans to deposit \\$ 100 into the fund at the end of each of the first 180 months. She then plans to deposit (\\$ 100+X) into the fund at the end of the last 120 months. Assume the fund earns interest at an annual effective rate of 4.01 \\%. Determine X.\nThe value of X=\\$ [ANS]?", "answer_v1": [ "606.69" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Hannah wishes to accumulate \\$ 175000 in a fund at the end of 25 years. She plans to deposit \\$ 70 into the fund at the end of each of the first 120 months. She then plans to deposit (\\$ 70+X) into the fund at the end of the last 180 months. Assume the fund earns interest at an annual effective rate of 1.33 \\%. Determine X.\nThe value of X=\\$ [ANS]?", "answer_v2": [ "754.55" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Hannah wishes to accumulate \\$ 140000 in a fund at the end of 25 years. She plans to deposit \\$ 80 into the fund at the end of each of the first 180 months. She then plans to deposit (\\$ 80+X) into the fund at the end of the last 120 months. Assume the fund earns interest at an annual effective rate of 2.25 \\%. Determine X.\nThe value of X=\\$ [ANS]?", "answer_v3": [ "803.76" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0112", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "3", "keywords": [ "financial mathematics", "interest", "future value" ], "problem_v1": "You make semiannual deposits of $\\\\$475.00$ into an ordinary annuity earning $5.79 \\%$ compounded semiannually. How much money is in the account after $10$ years? $[ANS]\nHow much interest did you earn in your first year? $[ANS]\n", "answer_v1": [ "12627.98", "13.75" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "You make semiannual deposits of $\\\\$580.00$ into an ordinary annuity earning $3.67 \\%$ compounded semiannually. How much money is in the account after $5$ years? $[ANS]\nHow much interest did you earn in your first year? $[ANS]\n", "answer_v2": [ "6303.14", "10.64" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "You make semiannual deposits of $\\\\$482.00$ into an ordinary annuity earning $4.25 \\%$ compounded semiannually. How much money is in the account after $13$ years? $[ANS]\nHow much interest did you earn in your first year? $[ANS]\n", "answer_v3": [ "16502.83", "10.24" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0113", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "3", "keywords": [ "financial mathematics", "interest", "future value" ], "problem_v1": "Liz and Bob just had a baby named Isabelle, and they want to save enough money for Isabelle to go to college. Assume that they start making monthly payments when Isabelle is $5$ into an ordinary annuity earning $5.62 \\%$, and they calculate that they will need $\\\\$28{,}300.00$ by the time Isabelle turns $18$. How much should they deposit every month so that they reach their goal? Deposit amount=$[ANS]\n", "answer_v1": [ "123.55" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Liz and Bob just had a baby named Isabelle, and they want to save enough money for Isabelle to go to college. Assume that they start making monthly payments when Isabelle is $8$ into an ordinary annuity earning $7.2 \\%$, and they calculate that they will need $\\\\$20{,}900.00$ by the time Isabelle turns $18$. How much should they deposit every month so that they reach their goal? Deposit amount=$[ANS]\n", "answer_v2": [ "119.43" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Liz and Bob just had a baby named Isabelle, and they want to save enough money for Isabelle to go to college. Assume that they start making monthly payments when Isabelle is $7$ into an ordinary annuity earning $5.73 \\%$, and they calculate that they will need $\\\\$23{,}400.00$ by the time Isabelle turns $18$. How much should they deposit every month so that they reach their goal? Deposit amount=$[ANS]\n", "answer_v3": [ "127.64" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0114", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "3", "keywords": [ "financial mathematics", "interest", "future value" ], "problem_v1": "John and Diane want to have $\\\\$358{,}000.00$ available for retirement. How much will they have to invest every month into an ordinary annuity earning an annual interest rate of $5.62 \\%$ compounded monthly if they invest for $8$ years? If they invest for $16$ years? If they invest for $26$ years? After $8$ years? $[ANS]\nAfter $16$ years? $[ANS]\nAfter $26$ years? $[ANS]\n", "answer_v1": [ "2962.04", "1154.32", "508.62" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "John and Diane want to have $\\\\$217{,}000.00$ available for retirement. How much will they have to invest every month into an ordinary annuity earning an annual interest rate of $7.2 \\%$ compounded monthly if they invest for $6$ years? If they invest for $14$ years? If they invest for $30$ years? After $6$ years? $[ANS]\nAfter $14$ years? $[ANS]\nAfter $30$ years? $[ANS]\n", "answer_v2": [ "2418.51", "751.79", "170.97" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "John and Diane want to have $\\\\$266{,}000.00$ available for retirement. How much will they have to invest every month into an ordinary annuity earning an annual interest rate of $5.73 \\%$ compounded monthly if they invest for $6$ years? If they invest for $14$ years? If they invest for $24$ years? After $6$ years? $[ANS]\nAfter $14$ years? $[ANS]\nAfter $24$ years? $[ANS]\n", "answer_v3": [ "3104.42", "1035.85", "431.59" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Financial_mathematics_0115", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "3", "keywords": [ "financial mathematics", "interest", "future value" ], "problem_v1": "John decides that he needs to save $\\\\$19{,}000.00$ in $6$ years to put towards a new vehicle.\n(a) How much should he invest every month into an ordinary annuity earning $2 \\%$ compounded monthly? $[ANS]\n Use this value in computing subsequent answers. (b) After 3 years of making payments, what is John's remaining balance? $[ANS]\n(c) Fill out the following lines of his balance sheet:\n$\\begin{array}{cccc}\\hline Period & Payment & Interest & Balance \\\\\\hline37 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline38 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline39 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline40 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline\\end{array}$\n", "answer_v1": [ "248.59", "9215.26", "248.59", "15.36", "9479.21", "248.59", "15.80", "9743.60", "248.59", "16.24", "10008.43", "248.59", "16.68", "10273.70" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [], [], [], [], [], [], [], [], [], [] ], "problem_v2": "John decides that he needs to save $\\\\$10{,}000.00$ in $5$ years to put towards a new vehicle.\n(a) How much should he invest every month into an ordinary annuity earning $2.42 \\%$ compounded monthly? $[ANS]\n Use this value in computing subsequent answers. (b) After 3 years of making payments, what is John's remaining balance? $[ANS]\n(c) Fill out the following lines of his balance sheet:\n$\\begin{array}{cccc}\\hline Period & Payment & Interest & Balance \\\\\\hline37 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline38 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline39 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline40 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline\\end{array}$\n", "answer_v2": [ "156.95", "5854.24", "156.95", "11.81", "6023.00", "156.95", "12.15", "6192.09", "156.95", "12.49", "6361.53", "156.95", "12.83", "6531.31" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [], [], [], [], [], [], [], [], [], [] ], "problem_v3": "John decides that he needs to save $\\\\$13{,}000.00$ in $5$ years to put towards a new vehicle.\n(a) How much should he invest every month into an ordinary annuity earning $2.03 \\%$ compounded monthly? $[ANS]\n Use this value in computing subsequent answers. (b) After 3 years of making payments, what is John's remaining balance? $[ANS]\n(c) Fill out the following lines of his balance sheet:\n$\\begin{array}{cccc}\\hline Period & Payment & Interest & Balance \\\\\\hline37 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline38 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline39 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline40 & $[ANS] & $[ANS] & $[ANS] \\\\\\hline\\end{array}$\n", "answer_v3": [ "206.04", "7641.30", "206.04", "12.93", "7860.26", "206.04", "13.30", "8079.60", "206.04", "13.67", "8299.31", "206.04", "14.04", "8519.39" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [], [], [], [], [], [], [], [], [], [] ] }, { "id": "Financial_mathematics_0116", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Sinking funds", "level": "3", "keywords": [ "financial mathematics", "interest", "future value" ], "problem_v1": "Tom and Sandy have set up a sinking fund in order to have $\\\\$20{,}000.00$ in $6$ years for their child's college education. How much should be paid monthly into an ordinary annuity earning $5.79 \\%$ compounded monthly so that they reach their goal? How much interest is earned during the last year? $[ANS]\n", "answer_v1": [ "232.98" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Tom and Sandy have set up a sinking fund in order to have $\\\\$15{,}000.00$ in $5$ years for their child's college education. How much should be paid monthly into an ordinary annuity earning $3.67 \\%$ compounded monthly so that they reach their goal? How much interest is earned during the last year? $[ANS]\n", "answer_v2": [ "228.14" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Tom and Sandy have set up a sinking fund in order to have $\\\\$17{,}000.00$ in $5$ years for their child's college education. How much should be paid monthly into an ordinary annuity earning $4.25 \\%$ compounded monthly so that they reach their goal? How much interest is earned during the last year? $[ANS]\n", "answer_v3": [ "254.79" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0117", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Mixed methods", "level": "5", "keywords": [ "financial mathematics", "annuities" ], "problem_v1": "Richard Gere has decided to give up acting and devote his life to the study of Buddhism. In order to provide for his future, he is going to deposit 50000 dollars each month for the next two years into an account. Immediately after his last deposit, he will spend three years in a Tibetan monastery. After leaving the monastery, he will begin making withdrawals from his account. He will make 24 equal annual withdrawals (that will deplete the account), the first coming on the day he leaves the monastery. If his account earns an interest rate of 9 percent convertible monthly for the entire life of the account, what will be the amount of each withdrawal?\nAnswer=[ANS] dollars.", "answer_v1": [ "166291.830477453" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Richard Gere has decided to give up acting and devote his life to the study of Buddhism. In order to provide for his future, he is going to deposit 50000 dollars each month for the next two years into an account. Immediately after his last deposit, he will spend three years in a Tibetan monastery. After leaving the monastery, he will begin making withdrawals from his account. He will make 29 equal annual withdrawals (that will deplete the account), the first coming on the day he leaves the monastery. If his account earns an interest rate of 6.3 percent convertible monthly for the entire life of the account, what will be the amount of each withdrawal?\nAnswer=[ANS] dollars.", "answer_v2": [ "111866.082805022" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Richard Gere has decided to give up acting and devote his life to the study of Buddhism. In order to provide for his future, he is going to deposit 50000 dollars each month for the next two years into an account. Immediately after his last deposit, he will spend three years in a Tibetan monastery. After leaving the monastery, he will begin making withdrawals from his account. He will make 24 equal annual withdrawals (that will deplete the account), the first coming on the day he leaves the monastery. If his account earns an interest rate of 7.2 percent convertible monthly for the entire life of the account, what will be the amount of each withdrawal?\nAnswer=[ANS] dollars.", "answer_v3": [ "134561.063385596" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0118", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Mixed methods", "level": "5", "keywords": [ "financial mathematics", "annuities" ], "problem_v1": "Ralph wants to quit his job and move to Hawaii on December 25, 2015. Once there, he anticipates that he will need to make annual withdrawals of 14500 dollars (starting on December 25, 2016) to supplement his income from working as a cabana boy, and he wants the money to last 10 years (i.e. he'll make 10 withdrawals total). His plan is to make annual deposits, starting on December 25, 2000 and ending on December 25, 2015, into an account paying 8.8 percent effective interest. How large should each deposit be for Ralph to realize his goal?\nAnswer=[ANS] dollars.", "answer_v1": [ "2893.35961747025" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Ralph wants to quit his job and move to Hawaii on December 25, 2015. Once there, he anticipates that he will need to make annual withdrawals of 12000 dollars (starting on December 25, 2016) to supplement his income from working as a cabana boy, and he wants the money to last 10 years (i.e. he'll make 10 withdrawals total). His plan is to make annual deposits, starting on December 25, 2000 and ending on December 25, 2015, into an account paying 9.8 percent effective interest. How large should each deposit be for Ralph to realize his goal?\nAnswer=[ANS] dollars.", "answer_v2": [ "2104.61633440047" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Ralph wants to quit his job and move to Hawaii on December 25, 2015. Once there, he anticipates that he will need to make annual withdrawals of 13000 dollars (starting on December 25, 2016) to supplement his income from working as a cabana boy, and he wants the money to last 10 years (i.e. he'll make 10 withdrawals total). His plan is to make annual deposits, starting on December 25, 2000 and ending on December 25, 2015, into an account paying 8.9 percent effective interest. How large should each deposit be for Ralph to realize his goal?\nAnswer=[ANS] dollars.", "answer_v3": [ "2560.76085256391" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0119", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Mixed methods", "level": "5", "keywords": [ "financial mathematics", "varying payments" ], "problem_v1": "Erin borrows 8500 dollars today, and agrees to repay the loan by making annual interest payments to the lender, and by also accumulating a sinking fund with increasing annual deposits to repay the principal. The interest rate on the loan is 9 percent, and the interest paid on the sinking fund is 6.5 percent, both effective. If the loan is to be settled 15 years from now, and the sinking fund deposits increase by 8 dollars per year, what is Erin's total outlay 6 years after taking out the loan? (Assume the first interest payment and sinking fund deposits are both due one year after taking out the loan.) Answer=[ANS] dollars.", "answer_v1": [ "1109.76533144622" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Erin borrows 7700 dollars today, and agrees to repay the loan by making annual interest payments to the lender, and by also accumulating a sinking fund with increasing annual deposits to repay the principal. The interest rate on the loan is 7.9 percent, and the interest paid on the sinking fund is 7.4 percent, both effective. If the loan is to be settled 20 years from now, and the sinking fund deposits increase by 5 dollars per year, what is Erin's total outlay 6 years after taking out the loan? (Assume the first interest payment and sinking fund deposits are both due one year after taking out the loan.) Answer=[ANS] dollars.", "answer_v2": [ "777.058084493044" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Erin borrows 8100 dollars today, and agrees to repay the loan by making annual interest payments to the lender, and by also accumulating a sinking fund with increasing annual deposits to repay the principal. The interest rate on the loan is 8.3 percent, and the interest paid on the sinking fund is 6.5 percent, both effective. If the loan is to be settled 14 years from now, and the sinking fund deposits increase by 6 dollars per year, what is Erin's total outlay 6 years after taking out the loan? (Assume the first interest payment and sinking fund deposits are both due one year after taking out the loan.) Answer=[ANS] dollars.", "answer_v3": [ "1041.47943683732" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0120", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Mixed methods", "level": "5", "keywords": [ "financial mathematics", "varying payments" ], "problem_v1": "Craig borrows 6500 dollars a year to pay for college expenses, starting on September 1, 2000-the day he starts college-and ending on September 1, 2004. (i.e. that's 5 withdrawals total). After graduation, he decides to go to graduate school in mathematics, and his loans are deferred (i.e. they still accrue interest, but no payments are due). After graduation from graduate school, he needs to begin paying off his loans. He will make monthly payments for 8 years, and each payment will increase by 2.2 percent. His payments will begin on July 1, 2007, exactly 6 years and 10 months after he started college. If he pays a nominal rate of 7.8 percent convertible monthly for the entire life of the loans, what will be the size of his first payment?\nAnswer=[ANS] dollars.", "answer_v1": [ "219.735438716594" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Craig borrows 4000 dollars a year to pay for college expenses, starting on September 1, 2000-the day he starts college-and ending on September 1, 2004. (i.e. that's 5 withdrawals total). After graduation, he decides to go to graduate school in mathematics, and his loans are deferred (i.e. they still accrue interest, but no payments are due). After graduation from graduate school, he needs to begin paying off his loans. He will make monthly payments for 12 years, and each payment will increase by 1.6 percent. His payments will begin on July 1, 2007, exactly 6 years and 10 months after he started college. If he pays a nominal rate of 6 percent convertible monthly for the entire life of the loans, what will be the size of his first payment?\nAnswer=[ANS] dollars.", "answer_v2": [ "77.3108495384998" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Craig borrows 5000 dollars a year to pay for college expenses, starting on September 1, 2000-the day he starts college-and ending on September 1, 2004. (i.e. that's 5 withdrawals total). After graduation, he decides to go to graduate school in mathematics, and his loans are deferred (i.e. they still accrue interest, but no payments are due). After graduation from graduate school, he needs to begin paying off his loans. He will make monthly payments for 7 years, and each payment will increase by 1.9 percent. His payments will begin on July 1, 2007, exactly 6 years and 10 months after he started college. If he pays a nominal rate of 6.6 percent convertible monthly for the entire life of the loans, what will be the size of his first payment?\nAnswer=[ANS] dollars.", "answer_v3": [ "224.312423198521" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0121", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Mixed methods", "level": "5", "keywords": [ "financial mathematics", "varying payments" ], "problem_v1": "Snoopy borrows 7100 dollars to pay for his new super-deluxe doghouse. To pay off the loan, he agrees to make monthly interest payments on the loan, and will also build up a sinking fund with equal monthly deposits to repay the principal with a single payment 27 months from now. If the interest rate on the loan is 9 percent, and the interest paid on the sinking fund is 6.6 percent, both nominal convertible monthly, what is Snoopy's total outlay? (Assume the first interest payment and the first sinking fund deposit will both come in one month.) Answer=[ANS] dollars.", "answer_v1": [ "297.892193661971" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Snoopy borrows 6600 dollars to pay for his new super-deluxe doghouse. To pay off the loan, he agrees to make monthly interest payments on the loan, and will also build up a sinking fund with equal monthly deposits to repay the principal with a single payment 24 months from now. If the interest rate on the loan is 7.9 percent, and the interest paid on the sinking fund is 7.5 percent, both nominal convertible monthly, what is Snoopy's total outlay? (Assume the first interest payment and the first sinking fund deposit will both come in one month.) Answer=[ANS] dollars.", "answer_v2": [ "299.197311500718" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Snoopy borrows 6800 dollars to pay for his new super-deluxe doghouse. To pay off the loan, he agrees to make monthly interest payments on the loan, and will also build up a sinking fund with equal monthly deposits to repay the principal with a single payment 25 months from now. If the interest rate on the loan is 8.3 percent, and the interest paid on the sinking fund is 6.6 percent, both nominal convertible monthly, what is Snoopy's total outlay? (Assume the first interest payment and the first sinking fund deposit will both come in one month.) Answer=[ANS] dollars.", "answer_v3": [ "301.507883157769" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0122", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Mixed methods", "level": "5", "keywords": [ "financial mathematics", "varying payments" ], "problem_v1": "To purchase a new couch that costs 2600 dollars, you set up a store credit card that charges interest at 16.8 percent convertible monthly, beginning immediately. Each month that you do not make a payment (starting one month after you purchase the couch), you are charged a 20 dollar fee that is added to your card balance. Due to financial difficulties, you cannot make a payment until 8 months after you purchase the couch. To pay off the card balance, you decide to make 23 monthly payments that increase by 4.5 percent per month. How much is your first payment?\nAnswer=[ANS] dollars.", "answer_v1": [ "93.4632221944138" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "To purchase a new couch that costs 1300 dollars, you set up a store credit card that charges interest at 18.9 percent convertible monthly, beginning immediately. Each month that you do not make a payment (starting one month after you purchase the couch), you are charged a 20 dollar fee that is added to your card balance. Due to financial difficulties, you cannot make a payment until 6 months after you purchase the couch. To pay off the card balance, you decide to make 30 monthly payments that increase by 3.8 percent per month. How much is your first payment?\nAnswer=[ANS] dollars.", "answer_v2": [ "36.66467968965" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "To purchase a new couch that costs 1700 dollars, you set up a store credit card that charges interest at 16.8 percent convertible monthly, beginning immediately. Each month that you do not make a payment (starting one month after you purchase the couch), you are charged a 20 dollar fee that is added to your card balance. Due to financial difficulties, you cannot make a payment until 7 months after you purchase the couch. To pay off the card balance, you decide to make 22 monthly payments that increase by 4 percent per month. How much is your first payment?\nAnswer=[ANS] dollars.", "answer_v3": [ "68.7892357395043" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0123", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Mixed methods", "level": "5", "keywords": [ "financial mathematics", "varying payments" ], "problem_v1": "Barry presently has 2.9 million dollars in an account paying a nominal rate of 8 percent convertible quarterly. He plans to start making quarterly withdrawals from the account when he retires, the first coming in exactly 19 years. If he would like to be able to make 92 withdrawals (with the last emptying the account) and the withdrawals will increase by 1.2 percent from one to the next, how large is his first withdrawal?\nAnswer=[ANS] dollars.", "answer_v1": [ "198775.986280974" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Barry presently has 1.9 million dollars in an account paying a nominal rate of 9 percent convertible quarterly. He plans to start making quarterly withdrawals from the account when he retires, the first coming in exactly 17 years. If he would like to be able to make 120 withdrawals (with the last emptying the account) and the withdrawals will increase by 0.8 percent from one to the next, how large is his first withdrawal?\nAnswer=[ANS] dollars.", "answer_v2": [ "149223.203934966" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Barry presently has 2.2 million dollars in an account paying a nominal rate of 8 percent convertible quarterly. He plans to start making quarterly withdrawals from the account when he retires, the first coming in exactly 18 years. If he would like to be able to make 88 withdrawals (with the last emptying the account) and the withdrawals will increase by 0.9 percent from one to the next, how large is his first withdrawal?\nAnswer=[ANS] dollars.", "answer_v3": [ "160562.588101496" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0124", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Mixed methods", "level": "5", "keywords": [ "financial mathematics", "sinking funds" ], "problem_v1": "Nicole borrows 258000 dollars for 10 years at a nominal rate of 6.9 percent convertible monthly. She has the option of paying off the loan using either the amortization or sinking fund method. If the sinking fund has an interest rate of 8.1 percent convertible monthly, how much will she save each month by going with the better method? (Assume monthly payments and deposits.) (Note: you'll need to decide which method is the better one.) Answer=[ANS] dollars.", "answer_v1": [ "96.4173730935559" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Nicole borrows 294000 dollars for 10 years at a nominal rate of 4.5 percent convertible monthly. She has the option of paying off the loan using either the amortization or sinking fund method. If the sinking fund has an interest rate of 5.7 percent convertible monthly, how much will she save each month by going with the better method? (Assume monthly payments and deposits.) (Note: you'll need to decide which method is the better one.) Answer=[ANS] dollars.", "answer_v2": [ "121.082286795423" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Nicole borrows 261000 dollars for 10 years at a nominal rate of 5.4 percent convertible monthly. She has the option of paying off the loan using either the amortization or sinking fund method. If the sinking fund has an interest rate of 6.6 percent convertible monthly, how much will she save each month by going with the better method? (Assume monthly payments and deposits.) (Note: you'll need to decide which method is the better one.) Answer=[ANS] dollars.", "answer_v3": [ "103.721377464596" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0125", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Mixed methods", "level": "5", "keywords": [ "financial mathematics", "sinking funds" ], "problem_v1": "Wanda takes out a 33-year mortgage for 158000 dollars at an interest rate of 8.4 percent effective. To repay the loan, she agrees to make equal monthly payments, the first coming in one month. However, after making the 10th payment, she decides to refinance the mortgage. In particular, she decides to make 97 more monthly payments (each of the same amount as before), and then she'll pay off the remainder of the loan with a large lump payment immediately after the last of these 97 payments. To save money for this large final payment, she plans to make equal monthly deposits into an account paying 5.4 percent convertible monthly. These deposits will occur at the same time as the monthly loan payments, i.e. the first deposit will be one month after she refinances the loan, and the last will be at the time of the final loan payment. (So there are a total of 97 deposits.) What will be the amount of each of the monthly deposits?\nAnswer=[ANS] dollars.", "answer_v1": [ "1199.79030774696" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Wanda takes out a 25-year mortgage for 194000 dollars at an interest rate of 6.9 percent effective. To repay the loan, she agrees to make equal monthly payments, the first coming in one month. However, after making the 10th payment, she decides to refinance the mortgage. In particular, she decides to make 93 more monthly payments (each of the same amount as before), and then she'll pay off the remainder of the loan with a large lump payment immediately after the last of these 93 payments. To save money for this large final payment, she plans to make equal monthly deposits into an account paying 6.3 percent convertible monthly. These deposits will occur at the same time as the monthly loan payments, i.e. the first deposit will be one month after she refinances the loan, and the last will be at the time of the final loan payment. (So there are a total of 93 deposits.) What will be the amount of each of the monthly deposits?\nAnswer=[ANS] dollars.", "answer_v2": [ "1331.68786007801" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Wanda takes out a 28-year mortgage for 161000 dollars at an interest rate of 7.2 percent effective. To repay the loan, she agrees to make equal monthly payments, the first coming in one month. However, after making the 10th payment, she decides to refinance the mortgage. In particular, she decides to make 95 more monthly payments (each of the same amount as before), and then she'll pay off the remainder of the loan with a large lump payment immediately after the last of these 95 payments. To save money for this large final payment, she plans to make equal monthly deposits into an account paying 5.4 percent convertible monthly. These deposits will occur at the same time as the monthly loan payments, i.e. the first deposit will be one month after she refinances the loan, and the last will be at the time of the final loan payment. (So there are a total of 95 deposits.) What will be the amount of each of the monthly deposits?\nAnswer=[ANS] dollars.", "answer_v3": [ "1172.06697112905" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0126", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Mixed methods", "level": "4", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "Mrs. Hart, at age 65, can expect to live for 25 years. If she can invest at 9\\% per annum compounded monthly, how much does she need now to guarantee herself \\$900 every month for the next 25 years? Answer=\\$ [ANS]", "answer_v1": [ "107245.45994239" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Mrs. Hart, at age 65, can expect to live for 25 years. If she can invest at 12\\% per annum compounded monthly, how much does she need now to guarantee herself \\$300 every month for the next 25 years? Answer=\\$ [ANS]", "answer_v2": [ "28483.9653764514" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Mrs. Hart, at age 65, can expect to live for 25 years. If she can invest at 9\\% per annum compounded monthly, how much does she need now to guarantee herself \\$500 every month for the next 25 years? Answer=\\$ [ANS]", "answer_v3": [ "59580.8110791057" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0127", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Mixed methods", "level": "5", "keywords": [ "payment amount" ], "problem_v1": "A college education fund is to be accumulated by twenty level semi-annual deposits, the first due on Juanary 1, 1996. The fund is to provide 16 quarterly withdrawals of \\$ 1800 each, the first due on October 1, 2005. Interest is compounded semiannually at an annual rate of 10 \\%. What is the amount of each semi-annual deposit?\nAmount of each semi-annual deposit=\\$ [ANS]?", "answer_v1": [ "712.36" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A college education fund is to be accumulated by twenty level semi-annual deposits, the first due on Juanary 1, 1996. The fund is to provide 16 quarterly withdrawals of \\$ 1000 each, the first due on October 1, 2005. Interest is compounded semiannually at an annual rate of 15 \\%. What is the amount of each semi-annual deposit?\nAmount of each semi-annual deposit=\\$ [ANS]?", "answer_v2": [ "275.5" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A college education fund is to be accumulated by twenty level semi-annual deposits, the first due on Juanary 1, 1996. The fund is to provide 16 quarterly withdrawals of \\$ 1300 each, the first due on October 1, 2005. Interest is compounded semiannually at an annual rate of 10 \\%. What is the amount of each semi-annual deposit?\nAmount of each semi-annual deposit=\\$ [ANS]?", "answer_v3": [ "514.48" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0128", "subject": "Financial_mathematics", "topic": "Annuities", "subtopic": "Mixed methods", "level": "3", "keywords": [ "financial mathematics", "interest", "future value" ], "problem_v1": "Bob makes his first $\\\\$1{,}100$ deposit into an IRA earning $7$ \\% compounded annually on the day he turns 25 and his last $\\\\$1{,}100$ deposit on the day he turns 50 (26 equal deposits in all.) With no additional deposits, the money in the IRA continues to earn $7$ \\% interest compounded annually until Bob retires on his 65th birthday. How much is the IRA worth when Bob retires? Value of the IRA on Bob's 65th birthday: $[ANS]\n", "answer_v1": [ "208428.60" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Bob makes his first $\\\\$750$ deposit into an IRA earning $8$ \\% compounded annually on the day he turns 22 and his last $\\\\$750$ deposit on the day he turns 42 (21 equal deposits in all.) With no additional deposits, the money in the IRA continues to earn $8$ \\% interest compounded annually until Bob retires on his 65th birthday. How much is the IRA worth when Bob retires? Value of the IRA on Bob's 65th birthday: $[ANS]\n", "answer_v2": [ "222042.26" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Bob makes his first $\\\\$900$ deposit into an IRA earning $7.5$ \\% compounded annually on the day he turns 23 and his last $\\\\$900$ deposit on the day he turns 46 (24 equal deposits in all.) With no additional deposits, the money in the IRA continues to earn $7.5$ \\% interest compounded annually until Bob retires on his 65th birthday. How much is the IRA worth when Bob retires? Value of the IRA on Bob's 65th birthday: $[ANS]\n", "answer_v3": [ "221577.75" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0129", "subject": "Financial_mathematics", "topic": "Bonds", "subtopic": "Prices and coupon rates", "level": "3", "keywords": [ "financial mathematics", "bonds" ], "problem_v1": "A 20-year bond with a face value of 1500 dollars is redeemable at twice par, and pays annual coupons at a rate of 4.2 percent effective. Find the price to yield an investor 5.4 percent effective. Answer=[ANS] dollars.", "answer_v1": [ "1807.03407052563" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A 14-year bond with a face value of 1500 dollars is redeemable at twice par, and pays annual coupons at a rate of 3.1 percent effective. Find the price to yield an investor 5.9 percent effective. Answer=[ANS] dollars.", "answer_v2": [ "1779.45831024084" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A 15-year bond with a face value of 1500 dollars is redeemable at twice par, and pays annual coupons at a rate of 3.5 percent effective. Find the price to yield an investor 5.5 percent effective. Answer=[ANS] dollars.", "answer_v3": [ "1870.77214385947" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0130", "subject": "Financial_mathematics", "topic": "Bonds", "subtopic": "Prices and coupon rates", "level": "4", "keywords": [ "financial mathematics", "bonds" ], "problem_v1": "Two 1000 dollar face value bonds are both redeemable at par, with the first having a redemption date 3 years prior to the redemption date of the second. Both are bought to yield 11.6 percent convertible semiannually. The first bond sells for 801.8 dollars and pays coupons at 8.2 precent convertible semiannually. The second bond pays coupons at 5.1 percent per half year. What is the price of the second bond? Answer=[ANS] dollars.", "answer_v1": [ "907.17" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Two 1000 dollar face value bonds are both redeemable at par, with the first having a redemption date 3 years prior to the redemption date of the second. Both are bought to yield 11.1 percent convertible semiannually. The first bond sells for 827.97 dollars and pays coupons at 7.8 precent convertible semiannually. The second bond pays coupons at 5.3 percent per half year. What is the price of the second bond? Answer=[ANS] dollars.", "answer_v2": [ "968.68" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Two 1000 dollar face value bonds are both redeemable at par, with the first having a redemption date 3 years prior to the redemption date of the second. Both are bought to yield 11.3 percent convertible semiannually. The first bond sells for 810.99 dollars and pays coupons at 7.9 precent convertible semiannually. The second bond pays coupons at 5.1 percent per half year. What is the price of the second bond? Answer=[ANS] dollars.", "answer_v3": [ "928.68" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0131", "subject": "Financial_mathematics", "topic": "Bonds", "subtopic": "Prices and coupon rates", "level": "3", "keywords": [ "finance", "bond" ], "problem_v1": "Ben Kerr is contemplating buying a zero coupon bond that matures in 11 years and has a face value of \\$18000. If the bond yields a return of 4.5\\% per year, how much should Ben pay for the bond? (Round your answer to 2 decimal places.) \\$ [ANS]", "answer_v1": [ "11091.58" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Ben Kerr is contemplating buying a zero coupon bond that matures in 8 years and has a face value of \\$10000. If the bond yields a return of 5\\% per year, how much should Ben pay for the bond? (Round your answer to 2 decimal places.) \\$ [ANS]", "answer_v2": [ "6768.39" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Ben Kerr is contemplating buying a zero coupon bond that matures in 9 years and has a face value of \\$13000. If the bond yields a return of 4.75\\% per year, how much should Ben pay for the bond? (Round your answer to 2 decimal places.) \\$ [ANS]", "answer_v3": [ "8561.64" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0132", "subject": "Financial_mathematics", "topic": "Bonds", "subtopic": "Prices and coupon rates", "level": "4", "keywords": [ "exponential model", "bond" ], "problem_v1": "A 8\\% bond with semiannual coupons has a face amount of \\$40,000,000 and is issued on October 17, 1991. The bond has a maturity date of October 17, 2021. Given the following nominal annual yield rates complete the table.\n$\\begin{array}{cc}\\hline nominal annual yield rate & Price of bond on issue date \\\\\\hline6\\% & [ANS] \\\\\\hline8\\% & [ANS] \\\\\\hline9\\% & [ANS] \\\\\\hline\\end{array}$", "answer_v1": [ "51070225.4664478", "40000000", "35872395.5923588" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Problem 1 2. ERROR caught by Translator while processing this problem", "answer_v2": [], "answer_type_v2": [], "options_v2": [], "problem_v3": "A 7\\% bond with semiannual coupons has a face amount of \\$40,000,000 and is issued on April 17, 1988. The bond has a maturity date of April 17, 2013. Given the following nominal annual yield rates complete the table.\n$\\begin{array}{cc}\\hline nominal annual yield rate & Price of bond on issue date \\\\\\hline5\\% & [ANS] \\\\\\hline7\\% & [ANS] \\\\\\hline11\\% & [ANS] \\\\\\hline\\end{array}$", "answer_v3": [ "51344924.6722169", "40000000", "26454785.6794288" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Financial_mathematics_0133", "subject": "Financial_mathematics", "topic": "Bonds", "subtopic": "Prices and coupon rates", "level": "2", "keywords": [ "financial mathematics", "compound interest" ], "problem_v1": "A zero coupon bond is a bond that is sold now at a discount and will pay its face value at some time in the future when it matures (no interest payments are made). Suppose that a zero coupon bond with a face value of $\\\\$6{,}050.00$ matures in $23$ years. What should the bond be sold for now if its rate of return is to be $5.49 \\%$ compounded weekly? $[ANS]\n", "answer_v1": [ "1712.62" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A zero coupon bond is a bond that is sold now at a discount and will pay its face value at some time in the future when it matures (no interest payments are made). Suppose that a zero coupon bond with a face value of $\\\\$2{,}000.00$ matures in $14$ years. What should the bond be sold for now if its rate of return is to be $7.591 \\%$ compounded semianually? $[ANS]\n", "answer_v2": [ "704.74" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A zero coupon bond is a bond that is sold now at a discount and will pay its face value at some time in the future when it matures (no interest payments are made). Suppose that a zero coupon bond with a face value of $\\\\$3{,}350.00$ matures in $17$ years. What should the bond be sold for now if its rate of return is to be $5.633 \\%$ compounded quarterly? [ANS]\n", "answer_v3": [ "1294.38" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0134", "subject": "Financial_mathematics", "topic": "Bonds", "subtopic": "Book value", "level": "4", "keywords": [ "financial mathematics", "book value" ], "problem_v1": "A 12-year bond with a face value of F dollars earns interest at 10 percent convertible semiannually and has a yield rate of 7.5 percent convertible semiannually. If the book value immediately after the 7th coupon payment is 1131.74 dollars, and the book value immediately after the 11th coupon payment is 1091.29 dollars, what is the face value? Answer=[ANS] dollars.", "answer_v1": [ "1040" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A 9-year bond with a face value of F dollars earns interest at 8.9 percent convertible semiannually and has a yield rate of 8 percent convertible semiannually. If the book value immediately after the 7th coupon payment is 1092.68 dollars, and the book value immediately after the 11th coupon payment is 1104.43 dollars, what is the face value? Answer=[ANS] dollars.", "answer_v2": [ "920" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A 10-year bond with a face value of F dollars earns interest at 9.3 percent convertible semiannually and has a yield rate of 7.5 percent convertible semiannually. If the book value immediately after the 7th coupon payment is 1013.69 dollars, and the book value immediately after the 11th coupon payment is 981.72 dollars, what is the face value? Answer=[ANS] dollars.", "answer_v3": [ "980" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0135", "subject": "Financial_mathematics", "topic": "Bonds", "subtopic": "Book value", "level": "3", "keywords": [ "exponential model", "bond" ], "problem_v1": "Dom purchased a 30-year 5.2\\% bond with annual coupons on July 18, 1998 for \\$51,000.\n(a) How much interest would it earn by July 2011? Answer: [ANS]\n(b) What would be the total amount accumulated on July 2028? Answer: [ANS]", "answer_v1": [ "34476", "130560" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Jake purchased a 25-year 6.2\\% bond with annual coupons on December 5, 1997 for \\$95,000.\n(a) How much interest would it earn by December 2009? Answer: [ANS]\n(b) What would be the total amount accumulated on December 2022? Answer: [ANS]", "answer_v2": [ "70680", "242250" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "David purchased a 30-year 4.4\\% bond with annual coupons on August 8, 1999 for \\$89,000.\n(a) How much interest would it earn by August 2014? Answer: [ANS]\n(b) What would be the total amount accumulated on August 2029? Answer: [ANS]", "answer_v3": [ "58740", "206480" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0136", "subject": "Financial_mathematics", "topic": "Bonds", "subtopic": "Book value", "level": "4", "keywords": [ "coupon", "par value" ], "problem_v1": "Sue purchased a 10-year par value bond with semiannual coupons at a nominal annual rate of 12 \\% convertible semiannually at a price of \\$ 1021.63. The bond can be called at par value X on any coupon date starting at the end of year 5. The price guarantees that Sue will receive a nominal annual rate of interest convertible semiannually of a least 16 \\%. Calculate X.\nPar value of bond, X=\\$ [ANS]", "answer_v1": [ "3136.21739205317" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Sue purchased a 10-year par value bond with semiannual coupons at a nominal annual rate of 3 \\% convertible semiannually at a price of \\$ 1028.64. The bond can be called at par value X on any coupon date starting at the end of year 5. The price guarantees that Sue will receive a nominal annual rate of interest convertible semiannually of a least 6 \\%. Calculate X.\nPar value of bond, X=\\$ [ANS]", "answer_v2": [ "752.295092444213" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Sue purchased a 10-year par value bond with semiannual coupons at a nominal annual rate of 6 \\% convertible semiannually at a price of \\$ 1022.11. The bond can be called at par value X on any coupon date starting at the end of year 5. The price guarantees that Sue will receive a nominal annual rate of interest convertible semiannually of a least 10 \\%. Calculate X.\nPar value of bond, X=\\$ [ANS]", "answer_v3": [ "1517.87259946715" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0137", "subject": "Financial_mathematics", "topic": "Bonds", "subtopic": "Other bonds", "level": "4", "keywords": [ "financial mathematics", "other bonds" ], "problem_v1": "A share of preferred stock pays dividends at a predetermined rate, and so can be thought of as a bond that pays coupons forever and has no redemption value. Suppose that such a share of stock pays semiannual dividends that increase by 2 percent with each dividend, and the first dividend is 9 dollars. If the price of the stock is 105 dollars, what is the yield rate? (Give your answer as the nominal rate convertible semiannually.) Answer=[ANS] percent.", "answer_v1": [ "21.1428571428571" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A share of preferred stock pays dividends at a predetermined rate, and so can be thought of as a bond that pays coupons forever and has no redemption value. Suppose that such a share of stock pays semiannual dividends that increase by 2.2 percent with each dividend, and the first dividend is 6 dollars. If the price of the stock is 86 dollars, what is the yield rate? (Give your answer as the nominal rate convertible semiannually.) Answer=[ANS] percent.", "answer_v2": [ "18.353488372093" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A share of preferred stock pays dividends at a predetermined rate, and so can be thought of as a bond that pays coupons forever and has no redemption value. Suppose that such a share of stock pays semiannual dividends that increase by 2.1 percent with each dividend, and the first dividend is 7 dollars. If the price of the stock is 91 dollars, what is the yield rate? (Give your answer as the nominal rate convertible semiannually.) Answer=[ANS] percent.", "answer_v3": [ "19.5846153846154" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0138", "subject": "Financial_mathematics", "topic": "Equations of value", "subtopic": "Dollar weighted rate of return", "level": "3", "keywords": [ "financial mathematics", "dollar weighted rate of return" ], "problem_v1": "Dennis invests 3600 dollars in a mutual fund on January 1. On May 1, his fund balance is 7600 dollars, and he withdraws 1300 dollars. On the following January 1, his fund balance is 3700 dollars. What is Dennis' dollar-weighted rate of return? (Assume simple interest and months of equal length.) Answer=[ANS] percent.", "answer_v1": [ "51.219512195122" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Dennis invests 2000 dollars in a mutual fund on January 1. On May 1, his fund balance is 8000 dollars, and he withdraws 1000 dollars. On the following January 1, his fund balance is 3300 dollars. What is Dennis' dollar-weighted rate of return? (Assume simple interest and months of equal length.) Answer=[ANS] percent.", "answer_v2": [ "172.5" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Dennis invests 2600 dollars in a mutual fund on January 1. On May 1, his fund balance is 7600 dollars, and he withdraws 1100 dollars. On the following January 1, his fund balance is 3600 dollars. What is Dennis' dollar-weighted rate of return? (Assume simple interest and months of equal length.) Answer=[ANS] percent.", "answer_v3": [ "112.5" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0139", "subject": "Financial_mathematics", "topic": "Equations of value", "subtopic": "Dollar weighted rate of return", "level": "3", "keywords": [ "financial mathematics", "dollar weighted rate of return" ], "problem_v1": "Bert invests 780 dollars now, and 560 dollars in 5 years. Ten years after the first investment, the accumulated value of the combined investments is 3680 dollars. What are the possible effective rates of interest? (If you find more than one, list them separated by commas.) Answer=[ANS] percent.", "answer_v1": [ "13.0016919988142" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Bert invests 700 dollars now, and 600 dollars in 5 years. Ten years after the first investment, the accumulated value of the combined investments is 3540 dollars. What are the possible effective rates of interest? (If you find more than one, list them separated by commas.) Answer=[ANS] percent.", "answer_v2": [ "13.2232999196952" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Bert invests 730 dollars now, and 560 dollars in 5 years. Ten years after the first investment, the accumulated value of the combined investments is 3580 dollars. What are the possible effective rates of interest? (If you find more than one, list them separated by commas.) Answer=[ANS] percent.", "answer_v3": [ "13.2624698615134" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0140", "subject": "Financial_mathematics", "topic": "Equations of value", "subtopic": "Dollar weighted rate of return", "level": "4", "keywords": [ "financial mathematics", "dollar weighted rate of return" ], "problem_v1": "Molly establishes a line of credit with a deposit of 1000 dollars. Two years later, she withdraws 600 dollars. Three years after that, she deposits 1600 dollars. Two years after that, she withdraws 900 dollars. Three years after that, she deposits 1600 dollars. Fifteen years after establishing the line of credit, she makes a withdrawal of 4500 dollars that closes the account. Let $i$ be the effective rate of interest. Set up an equation of value for this problem that would be used to solve for the possible effective rates of interest. Make the substitution $x=1+i$ to get an equation in the variable $x$. Fill in the missing portion of this equation below: Answer: [ANS] $=4500$.", "answer_v1": [ " 1000*x**15 - 600*x**13 + 1600*x**10 - 900*x**8 + 1600*x**5 " ], "answer_type_v1": [ "EX" ], "options_v1": [ [] ], "problem_v2": "Molly establishes a line of credit with a deposit of 1000 dollars. Two years later, she withdraws 200 dollars. Three years after that, she deposits 2000 dollars. Two years after that, she withdraws 500 dollars. Three years after that, she deposits 1000 dollars. Fifteen years after establishing the line of credit, she makes a withdrawal of 4500 dollars that closes the account. Let $i$ be the effective rate of interest. Set up an equation of value for this problem that would be used to solve for the possible effective rates of interest. Make the substitution $x=1+i$ to get an equation in the variable $x$. Fill in the missing portion of this equation below: Answer: [ANS] $=4500$.", "answer_v2": [ " 1000*x**15 - 200*x**13 + 2000*x**10 - 500*x**8 + 1000*x**5 " ], "answer_type_v2": [ "EX" ], "options_v2": [ [] ], "problem_v3": "Molly establishes a line of credit with a deposit of 1000 dollars. Two years later, she withdraws 350 dollars. Three years after that, she deposits 1600 dollars. Two years after that, she withdraws 600 dollars. Three years after that, she deposits 1300 dollars. Fifteen years after establishing the line of credit, she makes a withdrawal of 4500 dollars that closes the account. Let $i$ be the effective rate of interest. Set up an equation of value for this problem that would be used to solve for the possible effective rates of interest. Make the substitution $x=1+i$ to get an equation in the variable $x$. Fill in the missing portion of this equation below: Answer: [ANS] $=4500$.", "answer_v3": [ " 1000*x**15 - 350*x**13 + 1600*x**10 - 600*x**8 + 1300*x**5 " ], "answer_type_v3": [ "EX" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0141", "subject": "Financial_mathematics", "topic": "Equations of value", "subtopic": "Dollar weighted rate of return", "level": "4", "keywords": [ "financial mathematics", "dollar weighted rate of return" ], "problem_v1": "Batman has been offered the following investment opportunity. He promises to invest 10000 dollars now and 11877 dollars in two years, and in return will receive 21800 dollars in one year. What are the possible effective rates of interest? (If you find more than one, list them separated by commas.) Answer=[ANS] percent.", "answer_v1": [ "(7, 11)" ], "answer_type_v1": [ "UOL" ], "options_v1": [ [] ], "problem_v2": "Batman has been offered the following investment opportunity. He promises to invest 10000 dollars now and 11752 dollars in two years, and in return will receive 21700 dollars in one year. What are the possible effective rates of interest? (If you find more than one, list them separated by commas.) Answer=[ANS] percent.", "answer_v2": [ "(4, 13)" ], "answer_type_v2": [ "UOL" ], "options_v2": [ [] ], "problem_v3": "Batman has been offered the following investment opportunity. He promises to invest 10000 dollars now and 11760 dollars in two years, and in return will receive 21700 dollars in one year. What are the possible effective rates of interest? (If you find more than one, list them separated by commas.) Answer=[ANS] percent.", "answer_v3": [ "(5, 12)" ], "answer_type_v3": [ "UOL" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0142", "subject": "Financial_mathematics", "topic": "Equations of value", "subtopic": "Dollar weighted rate of return", "level": "3", "keywords": [ "financial mathematics", "dollar weighted rate of return" ], "problem_v1": "Suppose that you loan 450 dollars to a friend today, and 575 dollars to the same friend a year from now. In two years, you receive 1175 dollars repayment for both loans. What are the possible effective rates of interest on this transaction? (If you find more than one, list them separated by commas.) Answer=[ANS] percent.", "answer_v1": [ "9.87215747814902" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose that you loan 300 dollars to a friend today, and 675 dollars to the same friend a year from now. In two years, you receive 1125 dollars repayment for both loans. What are the possible effective rates of interest on this transaction? (If you find more than one, list them separated by commas.) Answer=[ANS] percent.", "answer_v2": [ "11.4559108396115" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose that you loan 350 dollars to a friend today, and 575 dollars to the same friend a year from now. In two years, you receive 1075 dollars repayment for both loans. What are the possible effective rates of interest on this transaction? (If you find more than one, list them separated by commas.) Answer=[ANS] percent.", "answer_v3": [ "11.4074843548461" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0143", "subject": "Financial_mathematics", "topic": "Equations of value", "subtopic": "Dollar weighted rate of return", "level": "3", "keywords": [ "financial mathematics", "dollar weighted rate of return" ], "problem_v1": "Two years ago, you invested 3800 dollars. Today, you invest an additional 2100 dollars in the same account. If the total value of the two investments two years from now is 8150 dollars, what are the possible nominal rates of interest convertible quarterly? (If you find more than one, list them separated by commas.) Answer=[ANS] percent.", "answer_v1": [ "9.81515901300183" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Two years ago, you invested 3000 dollars. Today, you invest an additional 2500 dollars in the same account. If the total value of the two investments two years from now is 7000 dollars, what are the possible nominal rates of interest convertible quarterly? (If you find more than one, list them separated by commas.) Answer=[ANS] percent.", "answer_v2": [ "7.78227085059235" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Two years ago, you invested 3300 dollars. Today, you invest an additional 2100 dollars in the same account. If the total value of the two investments two years from now is 7150 dollars, what are the possible nominal rates of interest convertible quarterly? (If you find more than one, list them separated by commas.) Answer=[ANS] percent.", "answer_v3": [ "8.69730118799987" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0144", "subject": "Financial_mathematics", "topic": "Equations of value", "subtopic": "Dollar weighted rate of return", "level": "4", "keywords": [ "financial mathematics", "dollar weighted rate of return" ], "problem_v1": "Mark invests 1000 dollars. Two years later, he receives a payment from the investment of 2520 dollars. Two years after that, he invests another 426.7 dollars, and two years after that, he adds 2923.2 dollars more to the investment. Two years later, he receives a final payment of 1840.57 dollars that closes out the investment. What are the possible effective rates of interest? (If you find more than one, list them separated by commas.) Answer(s)=[ANS] percent.", "answer_v1": [ "(10.9053650640942, 13.5781669160055, 3.78019856537666)" ], "answer_type_v1": [ "UOL" ], "options_v1": [ [] ], "problem_v2": "Mark invests 1000 dollars. Two years later, he receives a payment from the investment of 2380 dollars. Two years after that, he invests another 304.5 dollars, and two years after that, he adds 2641.8 dollars more to the investment. Two years later, he receives a final payment of 1570.1 dollars that closes out the investment. What are the possible effective rates of interest? (If you find more than one, list them separated by commas.) Answer(s)=[ANS] percent.", "answer_v2": [ "(7.23805294763609, 10.9053650640942, 2.64333272479387)" ], "answer_type_v2": [ "UOL" ], "options_v2": [ [] ], "problem_v3": "Mark invests 1000 dollars. Two years later, he receives a payment from the investment of 2420 dollars. Two years after that, he invests another 343.2 dollars, and two years after that, he adds 2710.4 dollars more to the investment. Two years later, he receives a final payment of 1638.78 dollars that closes out the investment. What are the possible effective rates of interest? (If you find more than one, list them separated by commas.) Answer(s)=[ANS] percent.", "answer_v3": [ "(8.62780491200215, 11.3552872566004, 2.87373447220802)" ], "answer_type_v3": [ "UOL" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0145", "subject": "Financial_mathematics", "topic": "Equations of value", "subtopic": "Dollar weighted rate of return", "level": "3", "keywords": [ "financial mathematics", "effective and nominal rates" ], "problem_v1": "On March 1, 2004, Audrey opens a savings account with a deposit of 2760 dollars. On March 1, 2007, she withdraws 620 dollars. On March 1, 2010, the balance in the account is 3800 dollars. What are the possible effective rates of interest for this account? (If you find more than one, list them separated by commas.) Answer=[ANS] percent.", "answer_v1": [ "8.88848879586868" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "On March 1, 2004, Audrey opens a savings account with a deposit of 2080 dollars. On March 1, 2007, she withdraws 690 dollars. On March 1, 2010, the balance in the account is 3560 dollars. What are the possible effective rates of interest for this account? (If you find more than one, list them separated by commas.) Answer=[ANS] percent.", "answer_v2": [ "14.07822050615" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "On March 1, 2004, Audrey opens a savings account with a deposit of 2310 dollars. On March 1, 2007, she withdraws 620 dollars. On March 1, 2010, the balance in the account is 3620 dollars. What are the possible effective rates of interest for this account? (If you find more than one, list them separated by commas.) Answer=[ANS] percent.", "answer_v3": [ "11.6877528450828" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0146", "subject": "Financial_mathematics", "topic": "Equations of value", "subtopic": "Time weighted rate of return", "level": "4", "keywords": [ "financial mathematics", "time weighted rate of return" ], "problem_v1": "Suppose that you open a mutual fund account with a deposit of 530 dollars. 6 months later, the fund balance is 620 dollars, and you withdraw 204 dollars. A year after the account was opened, your balance is $X$ dollars. If the dollar weighted and time weighted rates of return were the same, what is the rate of return? (Assume simple interest for the dollar weighted calculation.) Answer=[ANS] percent.", "answer_v1": [ "40.9090909090909" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose that you open a mutual fund account with a deposit of 550 dollars. 3 months later, the fund balance is 605 dollars, and you withdraw 180 dollars. A year after the account was opened, your balance is $X$ dollars. If the dollar weighted and time weighted rates of return were the same, what is the rate of return? (Assume simple interest for the dollar weighted calculation.) Answer=[ANS] percent.", "answer_v2": [ "57.1428571428572" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose that you open a mutual fund account with a deposit of 530 dollars. 4 months later, the fund balance is 610 dollars, and you withdraw 192 dollars. A year after the account was opened, your balance is $X$ dollars. If the dollar weighted and time weighted rates of return were the same, what is the rate of return? (Assume simple interest for the dollar weighted calculation.) Answer=[ANS] percent.", "answer_v3": [ "64.8648648648647" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0147", "subject": "Financial_mathematics", "topic": "Equations of value", "subtopic": "Time weighted rate of return", "level": "3", "keywords": [ "financial mathematics", "time weighted rate of return" ], "problem_v1": "Your grandmother gives you 3600 dollars for your birthday, which you invest in a mutual fund on January 1. On June 1, your fund balance is 7600 dollars, and you then deposit 1300 dollars (which you received for your high school graduation). On the following January 1, you calculate that your dollar-weighted rate of return for the year was 29 percent. What was your time-weighted rate of return for the year? Answer=[ANS] percent.", "answer_v1": [ "46.2102580108198" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Your grandmother gives you 2000 dollars for your birthday, which you invest in a mutual fund on January 1. On June 1, your fund balance is 8000 dollars, and you then deposit 1000 dollars (which you received for your high school graduation). On the following January 1, you calculate that your dollar-weighted rate of return for the year was 48.4 percent. What was your time-weighted rate of return for the year? Answer=[ANS] percent.", "answer_v2": [ "88.9037037037037" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Your grandmother gives you 2600 dollars for your birthday, which you invest in a mutual fund on January 1. On June 1, your fund balance is 7600 dollars, and you then deposit 1100 dollars (which you received for your high school graduation). On the following January 1, you calculate that your dollar-weighted rate of return for the year was 26.2 percent. What was your time-weighted rate of return for the year? Answer=[ANS] percent.", "answer_v3": [ "52.8506041850869" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0148", "subject": "Financial_mathematics", "topic": "Equations of value", "subtopic": "Time weighted rate of return", "level": "3", "keywords": [ "financial mathematics", "time weighted rate of return" ], "problem_v1": "Suzanne invests 5200 dollars in the Nguyen Mutual Fund on January 1. On March 1, her fund balance is 3400 dollars, and she invests an additional 1100 dollars. On October 1, her fund balance is 8700 dollars, and she then withdraws 1900 dollars. On the following January 1, her fund balance is 6200 dollars. What is Suzanne's time-weighted rate of return? Answer=[ANS] percent.", "answer_v1": [ "15.2564102564102" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suzanne invests 4200 dollars in the Nguyen Mutual Fund on January 1. On March 1, her fund balance is 3900 dollars, and she invests an additional 600 dollars. On October 1, her fund balance is 8100 dollars, and she then withdraws 2500 dollars. On the following January 1, her fund balance is 6200 dollars. What is Suzanne's time-weighted rate of return? Answer=[ANS] percent.", "answer_v2": [ "85.0510204081633" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suzanne invests 4500 dollars in the Nguyen Mutual Fund on January 1. On March 1, her fund balance is 3500 dollars, and she invests an additional 800 dollars. On October 1, her fund balance is 8400 dollars, and she then withdraws 1800 dollars. On the following January 1, her fund balance is 6300 dollars. What is Suzanne's time-weighted rate of return? Answer=[ANS] percent.", "answer_v3": [ "45.0317124735729" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0149", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "simple", "interest" ], "problem_v1": "Dave borrows 35000 dollars from Vinnie (a personal loan specialist) on October 6, 1999. If Vinnie charges 17.5 percent simple interest, how much will Dave owe on November 27, 1999? Answer=[ANS]", "answer_v1": [ "35872.602739726" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Dave borrows 21000 dollars from Vinnie (a personal loan specialist) on October 3, 1999. If Vinnie charges 19 percent simple interest, how much will Dave owe on November 25, 1999? Answer=[ANS]", "answer_v2": [ "21579.3698630137" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Dave borrows 26000 dollars from Vinnie (a personal loan specialist) on October 3, 1999. If Vinnie charges 17.5 percent simple interest, how much will Dave owe on November 26, 1999? Answer=[ANS]", "answer_v3": [ "26673.1506849315" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0150", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "simple", "interest" ], "problem_v1": "Alvin makes a deposit of 3500 dollars on April 18, 2001. How much is in the account on September 20, 2001, if the account pays 6.2 percent simple interest? Answer=[ANS] dollars.", "answer_v1": [ "3592.15068493151" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Alvin makes a deposit of 2100 dollars on April 8, 2001. How much is in the account on September 12, 2001, if the account pays 6.9 percent simple interest? Answer=[ANS] dollars.", "answer_v2": [ "2162.32684931507" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Alvin makes a deposit of 2600 dollars on April 10, 2001. How much is in the account on September 16, 2001, if the account pays 6.2 percent simple interest? Answer=[ANS] dollars.", "answer_v3": [ "2670.22136986301" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0151", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "simple", "interest" ], "problem_v1": "An investment pays simple interest, and quadruples in 13 years. What is the interest rate? Answer=[ANS] percent.", "answer_v1": [ "23.0769230769231" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "An investment pays simple interest, and doubles in 17 years. What is the interest rate? Answer=[ANS] percent.", "answer_v2": [ "5.88235294117647" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "An investment pays simple interest, and doubles in 13 years. What is the interest rate? Answer=[ANS] percent.", "answer_v3": [ "7.69230769230769" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0152", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "simple", "interest" ], "problem_v1": "George invests 3160 dollars at a simple interest rate of 10.8 percent. How much is his investment worth after 22 months? Answer=[ANS] dollars.", "answer_v1": [ "3785.68" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "George invests 3870 dollars at a simple interest rate of 7.4 percent. How much is his investment worth after 15 months? Answer=[ANS] dollars.", "answer_v2": [ "4227.975" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "George invests 3210 dollars at a simple interest rate of 8.5 percent. How much is his investment worth after 17 months? Answer=[ANS] dollars.", "answer_v3": [ "3596.5375" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0153", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "simple", "interest" ], "problem_v1": "Cathy makes a deposit of 4300 dollars into an account that pays 6.3 percent simple interest. How much is in the account 7 years later? Answer=[ANS] dollars.", "answer_v1": [ "6196.3" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Cathy makes a deposit of 2200 dollars into an account that pays 7.8 percent simple interest. How much is in the account 4 years later? Answer=[ANS] dollars.", "answer_v2": [ "2886.4" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Cathy makes a deposit of 2900 dollars into an account that pays 6.4 percent simple interest. How much is in the account 5 years later? Answer=[ANS] dollars.", "answer_v3": [ "3828" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0154", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "simple", "interest" ], "problem_v1": "Bill borrows 3500 dollars from Cosa Nostra Loans, who charge 5.2 percent simple annual interest. If he borrows the money on March 18, how much does he owe on August 20 of the same year? Answer=[ANS] dollars.", "answer_v1": [ "3577.28767123288" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Bill borrows 2100 dollars from Cosa Nostra Loans, who charge 5.9 percent simple annual interest. If he borrows the money on March 8, how much does he owe on August 12 of the same year? Answer=[ANS] dollars.", "answer_v2": [ "2153.29397260274" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Bill borrows 2600 dollars from Cosa Nostra Loans, who charge 5.2 percent simple annual interest. If he borrows the money on March 10, how much does he owe on August 16 of the same year? Answer=[ANS] dollars.", "answer_v3": [ "2658.89534246575" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0155", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "simple", "interest" ], "problem_v1": "Suppose that Jane borrows 8300 dollars from a bank on April 18 at an annual rate of 8.4 percent simple interest. How much does she owe on August 20 of the same year? Answer=[ANS] dollars.", "answer_v1": [ "8536.85698630137" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose that Jane borrows 6200 dollars from a bank on April 8 at an annual rate of 9.3 percent simple interest. How much does she owe on August 12 of the same year? Answer=[ANS] dollars.", "answer_v2": [ "6399.04547945205" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose that Jane borrows 6900 dollars from a bank on April 10 at an annual rate of 8.4 percent simple interest. How much does she owe on August 16 of the same year? Answer=[ANS] dollars.", "answer_v3": [ "7103.25698630137" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0156", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "3", "keywords": [ "equation", "solve", "word problem", "interest" ], "problem_v1": "Lily invested a total of ${\\\\$73{,}000}$ in two accounts. One account pays $5.6\\%$ interest annually; the other pays $6.3\\%$ interest annually. At the end of the year, Lily earned a total interest of ${\\\\$4{,}396}$. How much money did Lily invest in each account?\nLily invested $[ANS] in the $5.6\\%$ account. Lily invested $[ANS] in the $6.3\\%$ account.", "answer_v1": [ "29000", "44000" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Eric invested a total of ${\\\\$52{,}000}$ in two accounts. One account pays $7.2\\%$ interest annually; the other pays $4.9\\%$ interest annually. At the end of the year, Eric earned a total interest of ${\\\\$3{,}215}$. How much money did Eric invest in each account?\nEric invested $[ANS] in the $7.2\\%$ account. Eric invested $[ANS] in the $4.9\\%$ account.", "answer_v2": [ "29000", "23000" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Sydney invested a total of ${\\\\$59{,}000}$ in two accounts. One account pays $5.3\\%$ interest annually; the other pays $4.2\\%$ interest annually. At the end of the year, Sydney earned a total interest of ${\\\\$2{,}808}$. How much money did Sydney invest in each account?\nSydney invested $[ANS] in the $5.3\\%$ account. Sydney invested $[ANS] in the $4.2\\%$ account.", "answer_v3": [ "30000", "29000" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0157", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "equation", "solve", "word problem", "interest" ], "problem_v1": "Eric invested ${\\\\$18{,}000}$ in two accounts. At the end of a year, one account had made a $6\\%$ gain, and the other had made a $7\\%$ gain. All together, Eric\u2019s accounts earned ${\\\\$1{,}190}$ in interest. How much money did Eric invest in each account? The table below may help you organize information before you write an equation. If we let $x$ be the amount of money invested in the $6\\%$ account... $\\begin{array}{cccccc}\\hline & Rate & \\times & Principal &=& Interest \\\\\\hline 6\\%Investment & 0.06 & & x & & 0.06x \\\\\\hline 7\\%Investment & 0.07 & & 18000-x & & [ANS] \\\\\\hline\\end{array}$\nAccording to the table, the total interest that Eric earned is [ANS] dollars. Now set up and solve an equation to find how much Eric invested in each account.\nEric invested $[ANS] at $6\\%$ and $[ANS] at $7\\%$.", "answer_v1": [ "0.07*(18000-x)", "0.06*x+0.07*(18000-x)", "7000", "11000" ], "answer_type_v1": [ "EX", "EX", "NV", "NV" ], "options_v1": [ [], [], [], [] ], "problem_v2": "Hannah invested ${\\\\$10{,}000}$ in two accounts. At the end of a year, one account had made a $10\\%$ gain, and the other had made a $1\\%$ gain. All together, Hannah\u2019s accounts earned ${\\\\$640}$ in interest. How much money did Hannah invest in each account? The table below may help you organize information before you write an equation. If we let $x$ be the amount of money invested in the $10\\%$ account... $\\begin{array}{cccccc}\\hline & Rate & \\times & Principal &=& Interest \\\\\\hline 10\\%Investment & 0.1 & & x & & 0.1x \\\\\\hline 1\\%Investment & 0.01 & & 10000-x & & [ANS] \\\\\\hline\\end{array}$\nAccording to the table, the total interest that Hannah earned is [ANS] dollars. Now set up and solve an equation to find how much Hannah invested in each account.\nHannah invested $[ANS] at $10\\%$ and $[ANS] at $1\\%$.", "answer_v2": [ "0.01*(10000-x)", "0.1*x+0.01*(10000-x)", "6000", "4000" ], "answer_type_v2": [ "EX", "EX", "NV", "NV" ], "options_v2": [ [], [], [], [] ], "problem_v3": "Evan invested ${\\\\$13{,}000}$ in two accounts. At the end of a year, one account had made a $8\\%$ gain, and the other had made a $3\\%$ gain. All together, Evan\u2019s accounts earned ${\\\\$715}$ in interest. How much money did Evan invest in each account? The table below may help you organize information before you write an equation. If we let $x$ be the amount of money invested in the $8\\%$ account... $\\begin{array}{cccccc}\\hline & Rate & \\times & Principal &=& Interest \\\\\\hline 8\\%Investment & 0.08 & & x & & 0.08x \\\\\\hline 3\\%Investment & 0.03 & & 13000-x & & [ANS] \\\\\\hline\\end{array}$\nAccording to the table, the total interest that Evan earned is [ANS] dollars. Now set up and solve an equation to find how much Evan invested in each account.\nEvan invested $[ANS] at $8\\%$ and $[ANS] at $3\\%$.", "answer_v3": [ "0.03*(13000-x)", "0.08*x+0.03*(13000-x)", "6500", "6500" ], "answer_type_v3": [ "EX", "EX", "NV", "NV" ], "options_v3": [ [], [], [], [] ] }, { "id": "Financial_mathematics_0158", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "1", "keywords": [ "percent", "interest", "application", "multiply" ], "problem_v1": "You invested ${\\\\$7{,}700}$ into an account which pays $6\\%$ interest per year. How much interest will you earn after a year?\nYou will earn $[ANS] in interest after a year.", "answer_v1": [ "462" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "You invested ${\\\\$1{,}730}$ into an account which pays $9\\%$ interest per year. How much interest will you earn after a year?\nYou will earn $[ANS] in interest after a year.", "answer_v2": [ "155.70" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "You invested ${\\\\$3{,}790}$ into an account which pays $6\\%$ interest per year. How much interest will you earn after a year?\nYou will earn $[ANS] in interest after a year.", "answer_v3": [ "227.40" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0159", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "percent", "increase", "application", "divide", "add" ], "problem_v1": "Over the course of the last year, Fabrienne\u2019s investment account has grown by $6.7\\%$. Currently, Fabrienne has ${\\\\$8{,}215.90}$ in this account. What was the balance in her account one year ago, before this gain?\nOne year ago the balance was $[ANS].", "answer_v1": [ "7700" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Over the course of the last year, Tien\u2019s investment account has grown by $8.1\\%$. Currently, Tien has ${\\\\$1{,}945.80}$ in this account. What was the balance in his account one year ago, before this gain?\nOne year ago the balance was $[ANS].", "answer_v2": [ "1800" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Over the course of the last year, Dawn\u2019s investment account has grown by $6.3\\%$. Currently, Dawn has ${\\\\$4{,}039.40}$ in this account. What was the balance in her account one year ago, before this gain?\nOne year ago the balance was $[ANS].", "answer_v3": [ "3800" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0160", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "1", "keywords": [ "equation", "solve", "word problem", "interest" ], "problem_v1": "The following table demonstrates the relation between interest rate, principal investment, and amount of interest. Fill in the missing entries with expressions or numbers.\n$\\begin{array}{cccccc}\\hline & Rate & \\times & Principal &=& Interest \\\\\\hlineSolution 1 & 76\\% & & 100 & & 76 \\\\\\hlineSolution 2 & 67\\% & & 300 & & [ANS] \\\\\\hlineSolution 3 & 30\\% & & 37 & & [ANS] \\\\\\hlineSolution 4 & 6\\% & & 310 & & [ANS] \\\\\\hlineSolution 5 & 5.6\\% & & 280 & & [ANS] \\\\\\hlineSolution 6 & 5\\% & & x & & [ANS] \\\\\\hlineSolution 7 & 4.4\\% & & 3000-x & & [ANS] \\\\\\hline\\end{array}$", "answer_v1": [ "201", "11.1", "18.6", "15.68", "0.05*x", "0.044*(3000-x)" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "EX", "EX" ], "options_v1": [ [], [], [], [], [], [] ], "problem_v2": "The following table demonstrates the relation between interest rate, principal investment, and amount of interest. Fill in the missing entries with expressions or numbers.\n$\\begin{array}{cccccc}\\hline & Rate & \\times & Principal &=& Interest \\\\\\hlineSolution 1 & 19\\% & & 100 & & 19 \\\\\\hlineSolution 2 & 24\\% & & 900 & & [ANS] \\\\\\hlineSolution 3 & 30\\% & & 25 & & [ANS] \\\\\\hlineSolution 4 & 3\\% & & 370 & & [ANS] \\\\\\hlineSolution 5 & 1.6\\% & & 330 & & [ANS] \\\\\\hlineSolution 6 & 8\\% & & x & & [ANS] \\\\\\hlineSolution 7 & 2.2\\% & & 2000-x & & [ANS] \\\\\\hline\\end{array}$", "answer_v2": [ "216", "7.5", "11.1", "5.28", "0.08*x", "0.022*(2000-x)" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "EX", "EX" ], "options_v2": [ [], [], [], [], [], [] ], "problem_v3": "The following table demonstrates the relation between interest rate, principal investment, and amount of interest. Fill in the missing entries with expressions or numbers.\n$\\begin{array}{cccccc}\\hline & Rate & \\times & Principal &=& Interest \\\\\\hlineSolution 1 & 36\\% & & 100 & & 36 \\\\\\hlineSolution 2 & 45\\% & & 200 & & [ANS] \\\\\\hlineSolution 3 & 30\\% & & 45 & & [ANS] \\\\\\hlineSolution 4 & 9\\% & & 470 & & [ANS] \\\\\\hlineSolution 5 & 2.3\\% & & 270 & & [ANS] \\\\\\hlineSolution 6 & 1\\% & & x & & [ANS] \\\\\\hlineSolution 7 & 6.9\\% & & 4000-x & & [ANS] \\\\\\hline\\end{array}$", "answer_v3": [ "90", "13.5", "42.3", "6.21", "0.01*x", "0.069*(4000-x)" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "EX", "EX" ], "options_v3": [ [], [], [], [], [], [] ] }, { "id": "Financial_mathematics_0161", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "What are the proceeds for a discounted loan for \\$800 repaid in 13 months at 12\\%?\nProceeds=\\$ [ANS]", "answer_v1": [ "696" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "What are the proceeds for a discounted loan for \\$100 repaid in 18 months at 5\\%?\nProceeds=\\$ [ANS]", "answer_v2": [ "92.5" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "What are the proceeds for a discounted loan for \\$400 repaid in 13 months at 7\\%?\nProceeds=\\$ [ANS]", "answer_v3": [ "369.666666666667" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0162", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "Susan borrows \\$800 for 11 months at 12 $\\frac{1}{8}$ \\% per annum simple interest. What is the amount due? Amount=\\$ [ANS]", "answer_v1": [ "888.916667" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Susan borrows \\$100 for 17 months at 5 $\\frac{1}{8}$ \\% per annum simple interest. What is the amount due? Amount=\\$ [ANS]", "answer_v2": [ "107.260417" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Susan borrows \\$400 for 8 months at 7 $\\frac{1}{8}$ \\% per annum simple interest. What is the amount due? Amount=\\$ [ANS]", "answer_v3": [ "419" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0163", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "What is the interest if \\$800 is borrowed for 18 months at 9\\% simple interest?\nInterest=\\$ [ANS]", "answer_v1": [ "108" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "What is the interest if \\$100 is borrowed for 24 months at 5\\% simple interest?\nInterest=\\$ [ANS]", "answer_v2": [ "10" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "What is the interest if \\$400 is borrowed for 18 months at 6\\% simple interest?\nInterest=\\$ [ANS]", "answer_v3": [ "36" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0164", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "Charlie wants to buy a \\$800 stereo set in 15 weeks. How much should he invest now at 12\\% simple interest to have the money in 15 weeks? Investment=\\$ [ANS]", "answer_v1": [ "773.234200743494" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Charlie wants to buy a \\$100 stereo set in 21 weeks. How much should he invest now at 5\\% simple interest to have the money in 21 weeks? Investment=\\$ [ANS]", "answer_v2": [ "98.0207351555137" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Charlie wants to buy a \\$400 stereo set in 15 weeks. How much should he invest now at 7\\% simple interest to have the money in 15 weeks? Investment=\\$ [ANS]", "answer_v3": [ "392.082940622055" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0165", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "A toy store owner would like to borrow \\$20000 from a bank to increase her stock. The bank will give the owner a discounted loan for 6 months at an interest rate of 13\\%. What maturity value should be used so that the owner will receive \\$20000?\nMaturity Value=\\$ [ANS]", "answer_v1": [ "21390.3743315508" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A toy store owner would like to borrow \\$5000 from a bank to increase her stock. The bank will give the owner a discounted loan for 9 months at an interest rate of 10\\%. What maturity value should be used so that the owner will receive \\$5000?\nMaturity Value=\\$ [ANS]", "answer_v2": [ "5405.4054054054" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A toy store owner would like to borrow \\$10000 from a bank to increase her stock. The bank will give the owner a discounted loan for 8 months at an interest rate of 10\\%. What maturity value should be used so that the owner will receive \\$10000?\nMaturity Value=\\$ [ANS]", "answer_v3": [ "10714.2857142857" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0166", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "percent" ], "problem_v1": "Find the length of the loan in months, if \\$800 is borrowed with an annual simple interest rate of 12\\% and with \\$888 repaid at the end of the loan. Length of the loan=[ANS] months.", "answer_v1": [ "11" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Find the length of the loan in months, if \\$100 is borrowed with an annual simple interest rate of 4\\% and with \\$105.666666666667 repaid at the end of the loan. Length of the loan=[ANS] months.", "answer_v2": [ "17" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Find the length of the loan in months, if \\$400 is borrowed with an annual simple interest rate of 6\\% and with \\$424 repaid at the end of the loan. Length of the loan=[ANS] months.", "answer_v3": [ "12" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0167", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "percent" ], "problem_v1": "Consider a discounted loan of \\$800, where the proceeds equal \\$635.33. The loan is repaid at the end of 19 months. Find the annual simple discount rate.\nAnnual simple discount rate=[ANS] \\%", "answer_v1": [ "13" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Consider a discounted loan of \\$100, where the proceeds equal \\$94.33. The loan is repaid at the end of 17 months. Find the annual simple discount rate.\nAnnual simple discount rate=[ANS] \\%", "answer_v2": [ "4" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Consider a discounted loan of \\$400, where the proceeds equal \\$355.66. The loan is repaid at the end of 19 months. Find the annual simple discount rate.\nAnnual simple discount rate=[ANS] \\%", "answer_v3": [ "7" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0168", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "equation of value", "time value of money", "simple interest rate" ], "problem_v1": "An investment fund has a value of \\$ 3000 at the beginning and the end of the year. A deposit of \\$ 558 was made at the end of four months. A withdrawal of \\$ 905 was made at the end of seven months. Find the rate of interest earned by the fund assuming simple interest during the year.\nAnnual simple interest rate=[ANS] \\%?", "answer_v1": [ "11.5862990066502" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "An investment fund has a value of \\$ 300 at the beginning and the end of the year. A deposit of \\$ 60 was made at the end of four months. A withdrawal of \\$ 78 was made at the end of seven months. Find the rate of interest earned by the fund assuming simple interest during the year.\nAnnual simple interest rate=[ANS] \\%?", "answer_v2": [ "5.85365853658537" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "An investment fund has a value of \\$ 1200 at the beginning and the end of the year. A deposit of \\$ 224 was made at the end of four months. A withdrawal of \\$ 328 was made at the end of seven months. Find the rate of interest earned by the fund assuming simple interest during the year.\nAnnual simple interest rate=[ANS] \\%?", "answer_v3": [ "8.5761407366685" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0169", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "3", "keywords": [ "functions", "algebra", "application of linear equations", "simple interest rate" ], "problem_v1": "Clare borrowed money from her parents at $7.3$ \\% simple interest to help pay her tuition. At the end of 1 year, she owed a total of $\\\\$2{,}440.00$ in principal and interest. How much did she borrow? Amount Borrowed: $[ANS] (Round your answer to the nearest cent and include units.)", "answer_v1": [ "2274.00" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Clare borrowed money from her parents at $7.7$ \\% simple interest to help pay her tuition. At the end of 1 year, she owed a total of $\\\\$2{,}140.00$ in principal and interest. How much did she borrow? Amount Borrowed: $[ANS] (Round your answer to the nearest cent and include units.)", "answer_v2": [ "1987.00" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Clare borrowed money from her parents at $4.0$ \\% simple interest to help pay her tuition. At the end of 1 year, she owed a total of $\\\\$1{,}820.00$ in principal and interest. How much did she borrow? Amount Borrowed: $[ANS] (Round your answer to the nearest cent and include units.)", "answer_v3": [ "1750.00" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0170", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "financial mathematics", "simple interest" ], "problem_v1": "A credit card company charges $28.3 \\%$ simple interest on overdue accounts. How much interest will be owed on a $\\\\$1{,}750.00$ account that is $55$ days overdue? $[ANS]\n", "answer_v1": [ "75.66" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A credit card company charges $31.9 \\%$ simple interest on overdue accounts. How much interest will be owed on a $\\\\$1{,}075.00$ account that is $30$ days overdue? $[ANS]\n", "answer_v2": [ "28.58" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A credit card company charges $28.6 \\%$ simple interest on overdue accounts. How much interest will be owed on a $\\\\$1{,}300.00$ account that is $40$ days overdue? $[ANS]\n", "answer_v3": [ "41.31" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0171", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "3", "keywords": [ "financial mathematics", "simple interest" ], "problem_v1": "A department store charges $\\\\$39.50$ interest for an account which owed $\\\\$550.00$ and was 81 days late. What is the annual simple interest rate that the department store is charging? [ANS] $\\%$ (Note: Your answer must be accurate to two decimal places)", "answer_v1": [ "32.3625" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A department store charges $\\\\$48.50$ interest for an account which owed $\\\\$410.00$ and was 57 days late. What is the annual simple interest rate that the department store is charging? [ANS] $\\%$ (Note: Your answer must be accurate to two decimal places)", "answer_v2": [ "75.7488" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A department store charges $\\\\$40.00$ interest for an account which owed $\\\\$460.00$ and was 64 days late. What is the annual simple interest rate that the department store is charging? [ANS] $\\%$ (Note: Your answer must be accurate to two decimal places)", "answer_v3": [ "49.5924" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0172", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "financial mathematics", "simple interest" ], "problem_v1": "If Greg borrows $\\\\$140.00$ from the bank at $7.1 \\%$ exact simple interest, how much interest does Greg owe if he pays back the money after 210 days? $[ANS]\n", "answer_v1": [ "5.72" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "If Greg borrows $\\\\$100.00$ from the bank at $7.5 \\%$ exact simple interest, how much interest does Greg owe if he pays back the money after 160 days? $[ANS]\n", "answer_v2": [ "3.29" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "If Greg borrows $\\\\$115.00$ from the bank at $7.1 \\%$ exact simple interest, how much interest does Greg owe if he pays back the money after 180 days? $[ANS]\n", "answer_v3": [ "4.03" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0173", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "financial mathematics", "simple interest" ], "problem_v1": "Tim needs $\\\\$6{,}400.00$ to remodel his bathroom. A remodeling company agrees to do the work in $135$ days. How much should he invest at $3.16 \\%$ exact simple interest to have the money in time? $[ANS]\n", "answer_v1": [ "6326.06" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Tim needs $\\\\$3{,}300.00$ to remodel his bathroom. A remodeling company agrees to do the work in $60$ days. How much should he invest at $3.87 \\%$ exact simple interest to have the money in time? $[ANS]\n", "answer_v2": [ "3279.14" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Tim needs $\\\\$4{,}400.00$ to remodel his bathroom. A remodeling company agrees to do the work in $75$ days. How much should he invest at $3.21 \\%$ exact simple interest to have the money in time? $[ANS]\n", "answer_v3": [ "4371.17" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0174", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "financial mathematics", "simple interest" ], "problem_v1": "If a $235$-day T-bill earns an annual simple interest of $3.863 \\%$ and has a maturity value of $\\\\$9{,}000.00$, what is the purchase price of the T-bill? $[ANS]\n", "answer_v1": [ "8778.63" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "If a $180$-day T-bill earns an annual simple interest of $2.448 \\%$ and has a maturity value of $\\\\$8{,}500.00$, what is the purchase price of the T-bill? $[ANS]\n", "answer_v2": [ "8397.22" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "If a $210$-day T-bill earns an annual simple interest of $2.836 \\%$ and has a maturity value of $\\\\$8{,}700.00$, what is the purchase price of the T-bill? $[ANS]\n", "answer_v3": [ "8558.42" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0175", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "financial mathematics", "simple interest" ], "problem_v1": "If $\\\\$6{,}264.00$ is loaned for $7$ months at an annual simple interest rate of $4.5 \\%$, how much interest is earned? $[ANS]\n", "answer_v1": [ "164.43" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "If $\\\\$2{,}915.00$ is loaned for $11$ months at an annual simple interest rate of $2.5 \\%$, how much interest is earned? $[ANS]\n", "answer_v2": [ "66.80" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "If $\\\\$4{,}067.00$ is loaned for $8$ months at an annual simple interest rate of $3 \\%$, how much interest is earned? $[ANS]\n", "answer_v3": [ "81.34" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0176", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "3", "keywords": [ "financial mathematics", "simple interest" ], "problem_v1": "An investment firm charges commissions on stock trades according to the following commission schedule:\n$\\begin{array}{cc}\\hline Transaction SizeTransaction Size & CommissionCommission \\\\\\hline\\$ 0-\\$ 1999.99 & \\$ 17+2.3 \\%of principal \\\\\\hline\\$ 2000-\\$ 3999.99 & \\$ 24+1.8 \\%of principal \\\\\\hline\\$ 4000-\\$ 5999.99 & \\$ 35+1.1 \\%of principal \\\\\\hline\\end{array}$\nSuppose an investor purchases $91$ stocks at $\\\\$14.47$ per share, holds for $32$ weeks and then sells the stocks for \\$ $\\\\$27.88$ per share. Find the annual simple interest rate earned by this investment. [ANS] $\\%$ (Note: Your answer should be correct to two decimal places to be counted as correct.)", "answer_v1": [ "142.324" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "An investment firm charges commissions on stock trades according to the following commission schedule:\n$\\begin{array}{cc}\\hline Transaction SizeTransaction Size & CommissionCommission \\\\\\hline\\$ 0-\\$ 1999.99 & \\$ 15+2.2 \\%of principal \\\\\\hline\\$ 2000-\\$ 3999.99 & \\$ 23+2 \\%of principal \\\\\\hline\\$ 4000-\\$ 5999.99 & \\$ 37+1.1 \\%of principal \\\\\\hline\\end{array}$\nSuppose an investor purchases $78$ stocks at $\\\\$14.91$ per share, holds for $26$ weeks and then sells the stocks for \\$ $\\\\$26.87$ per share. Find the annual simple interest rate earned by this investment. [ANS] $\\%$ (Note: Your answer should be correct to two decimal places to be counted as correct.)", "answer_v2": [ "151.419" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "An investment firm charges commissions on stock trades according to the following commission schedule:\n$\\begin{array}{cc}\\hline Transaction SizeTransaction Size & CommissionCommission \\\\\\hline\\$ 0-\\$ 1999.99 & \\$ 19+2.2 \\%of principal \\\\\\hline\\$ 2000-\\$ 3999.99 & \\$ 25+1.7 \\%of principal \\\\\\hline\\$ 4000-\\$ 5999.99 & \\$ 42+1.2 \\%of principal \\\\\\hline\\end{array}$\nSuppose an investor purchases $82$ stocks at $\\\\$14.50$ per share, holds for $28$ weeks and then sells the stocks for \\$ $\\\\$27.22$ per share. Find the annual simple interest rate earned by this investment. [ANS] $\\%$ (Note: Your answer should be correct to two decimal places to be counted as correct.)", "answer_v3": [ "152.108" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0177", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "3", "keywords": [ "financial mathematics", "interest", "simple" ], "problem_v1": "For services rendered, an attorney accepts a $240$ day note for $\\\\$5{,}250$ at $11$ \\% simple interest from a client. (Both interest and principal will be repaid at the end of $240$ days.) Wishing to be able to use her money sooner, the attorney sells the note to a third party for $\\\\$5{,}339.83$ after $80$ days. What annual interest rate will the third party receive for the investment? (Enter your answer as a percentage correct to three decimal places.) Annual simple interest rate for third party: [ANS] \\% Note: Be sure that your answer is correct to three decimal places, and that it is expressed as a percentage (e.g. if the answer is 9.123 \\% enter 9.123) into the answer box.", "answer_v1": [ "12.437" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "For services rendered, an attorney accepts a $90$ day note for $\\\\$4{,}250$ at $15$ \\% simple interest from a client. (Both interest and principal will be repaid at the end of $90$ days.) Wishing to be able to use her money sooner, the attorney sells the note to a third party for $\\\\$4{,}271.25$ after $30$ days. What annual interest rate will the third party receive for the investment? (Enter your answer as a percentage correct to three decimal places.) Annual simple interest rate for third party: [ANS] \\% Note: Be sure that your answer is correct to three decimal places, and that it is expressed as a percentage (e.g. if the answer is 9.123 \\% enter 9.123) into the answer box.", "answer_v2": [ "19.403" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "For services rendered, an attorney accepts a $120$ day note for $\\\\$4{,}500$ at $11$ \\% simple interest from a client. (Both interest and principal will be repaid at the end of $120$ days.) Wishing to be able to use her money sooner, the attorney sells the note to a third party for $\\\\$4{,}527.50$ after $40$ days. What annual interest rate will the third party receive for the investment? (Enter your answer as a percentage correct to three decimal places.) Annual simple interest rate for third party: [ANS] \\% Note: Be sure that your answer is correct to three decimal places, and that it is expressed as a percentage (e.g. if the answer is 9.123 \\% enter 9.123) into the answer box.", "answer_v3": [ "13.666" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0178", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "3", "keywords": [ "financial mathematics", "simple interest" ], "problem_v1": "Dave borrowed money from Tom, and they agreed that Dave would pay $\\\\$0.11$ per day for every \\$ $200$ borrowed. If Dave borrowed $\\\\$2{,}200.00$ for $80$ days, what amount will he repay, and what annual simple interest rate is Tom actually charging? [ANS] $\\%$ (Note: Your answer should be correct to two decimal places to be counted as correct.)", "answer_v1": [ "19.8" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Dave borrowed money from Tom, and they agreed that Dave would pay $\\\\$0.02$ per day for every \\$ $200$ borrowed. If Dave borrowed $\\\\$3{,}000.00$ for $55$ days, what amount will he repay, and what annual simple interest rate is Tom actually charging? [ANS] $\\%$ (Note: Your answer should be correct to two decimal places to be counted as correct.)", "answer_v2": [ "3.6" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Dave borrowed money from Tom, and they agreed that Dave would pay $\\\\$0.05$ per day for every \\$ $200$ borrowed. If Dave borrowed $\\\\$2{,}200.00$ for $65$ days, what amount will he repay, and what annual simple interest rate is Tom actually charging? [ANS] $\\%$ (Note: Your answer should be correct to two decimal places to be counted as correct.)", "answer_v3": [ "9" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0179", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "3", "keywords": [ "financial mathematics", "simple interest" ], "problem_v1": "Donna borrows $\\\\$4{,}029.10$ from her sister, Dawn, and Dawn accepts a $239$-day note at $13.8 \\%$ exact simple interest. After $69$ days, Dawn needs the money, and sells the note to a third party for $\\\\$4{,}213.00$. What exact simple interest rate will the third party receive for the investment? [ANS] $\\%$ (Note: Your answer should be accurate to two decimal places)", "answer_v1": [ "9.18226" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Donna borrows $\\\\$4{,}046.60$ from her sister, Dawn, and Dawn accepts a $223$-day note at $12.4 \\%$ exact simple interest. After $89$ days, Dawn needs the money, and sells the note to a third party for $\\\\$4{,}179.00$. What exact simple interest rate will the third party receive for the investment? [ANS] $\\%$ (Note: Your answer should be accurate to two decimal places)", "answer_v2": [ "11.3522" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Donna borrows $\\\\$4{,}030.30$ from her sister, Dawn, and Dawn accepts a $232$-day note at $12.8 \\%$ exact simple interest. After $66$ days, Dawn needs the money, and sells the note to a third party for $\\\\$4{,}190.00$. What exact simple interest rate will the third party receive for the investment? [ANS] $\\%$ (Note: Your answer should be accurate to two decimal places)", "answer_v3": [ "8.82671" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0180", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "financial mathematics", "simple interest" ], "problem_v1": "Many tax preparation firms offer their clients a refund anticipation loan (RAL). For a fee, the firm will give the client their refund on the day the return is filed. The loan is repaid when the IRS send the refund directly to the firm. Thus, the RAL fee is equivalent to the interest charge for the loan. The RAL schedule for a certain lender is below:\n$\\begin{array}{cc}\\hline RAL AmountRAL Amount & RAL FEERAL FEE \\\\\\hline\\$ 0-\\$ 999.99 & \\$ 21 \\\\\\hline\\$ 1,000-\\$ 1,999.99 & \\$ 31 \\\\\\hline\\$ 2,000-\\$ 2,999.99 & \\$ 46 \\\\\\hline\\$ 3,000-\\$ 3,999.99 & \\$ 61 \\\\\\hline\\$ 4,000-\\$ 4,999.99 & \\$ 81 \\\\\\hline\\end{array}$\nA client receives a $\\\\$3{,}768.00$ RAL which is repaid in $24$ days. What is the annual simple interest rate for this loan? [ANS] $\\%$ (Note: Your answer should be accurate to two decimal places)", "answer_v1": [ "24.2834" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Many tax preparation firms offer their clients a refund anticipation loan (RAL). For a fee, the firm will give the client their refund on the day the return is filed. The loan is repaid when the IRS send the refund directly to the firm. Thus, the RAL fee is equivalent to the interest charge for the loan. The RAL schedule for a certain lender is below:\n$\\begin{array}{cc}\\hline RAL AmountRAL Amount & RAL FEERAL FEE \\\\\\hline\\$ 0-\\$ 999.99 & \\$ 17 \\\\\\hline\\$ 1,000-\\$ 1,999.99 & \\$ 27 \\\\\\hline\\$ 2,000-\\$ 2,999.99 & \\$ 42 \\\\\\hline\\$ 3,000-\\$ 3,999.99 & \\$ 57 \\\\\\hline\\$ 4,000-\\$ 4,999.99 & \\$ 77 \\\\\\hline\\end{array}$\nA client receives a $\\\\$3{,}164.00$ RAL which is repaid in $29$ days. What is the annual simple interest rate for this loan? [ANS] $\\%$ (Note: Your answer should be accurate to two decimal places)", "answer_v2": [ "22.3637" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Many tax preparation firms offer their clients a refund anticipation loan (RAL). For a fee, the firm will give the client their refund on the day the return is filed. The loan is repaid when the IRS send the refund directly to the firm. Thus, the RAL fee is equivalent to the interest charge for the loan. The RAL schedule for a certain lender is below:\n$\\begin{array}{cc}\\hline RAL AmountRAL Amount & RAL FEERAL FEE \\\\\\hline\\$ 0-\\$ 999.99 & \\$ 18 \\\\\\hline\\$ 1,000-\\$ 1,999.99 & \\$ 28 \\\\\\hline\\$ 2,000-\\$ 2,999.99 & \\$ 43 \\\\\\hline\\$ 3,000-\\$ 3,999.99 & \\$ 58 \\\\\\hline\\$ 4,000-\\$ 4,999.99 & \\$ 78 \\\\\\hline\\end{array}$\nA client receives a $\\\\$3{,}372.00$ RAL which is repaid in $24$ days. What is the annual simple interest rate for this loan? [ANS] $\\%$ (Note: Your answer should be accurate to two decimal places)", "answer_v3": [ "25.8007" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0181", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "2", "keywords": [ "financial mathematics", "simple interest" ], "problem_v1": "If Laura invests $\\\\$1{,}380.00$ in an account earning $6.6 \\%$ simple interest, how much money will be her account after $3$ years? After $8$ years? After $3$ years: $[ANS]\nAfter $8$ years: $[ANS]\n", "answer_v1": [ "1653.24", "2108.64" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "If Laura invests $\\\\$1{,}040.00$ in an account earning $9.05 \\%$ simple interest, how much money will be her account after $2$ years? After $7$ years? After $2$ years: $[ANS]\nAfter $7$ years: $[ANS]\n", "answer_v2": [ "1228.24", "1698.84" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "If Laura invests $\\\\$1{,}150.00$ in an account earning $6.75 \\%$ simple interest, how much money will be her account after $2$ years? After $8$ years? After $2$ years: $[ANS]\nAfter $8$ years: $[ANS]\n", "answer_v3": [ "1305.25", "1771.00" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0182", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Simple interest", "level": "3", "keywords": [ "financial mathematics", "simple interest" ], "problem_v1": "After buying a new car, Jim decides to sell his old car to a friend Mark. Jim accepts a $142$ day note for $\\\\$6{,}658.16$ at $7.9 \\%$ exact simple interest as payment (both principal and interest will be paid at the end of $142$ days). $94$ days later, Jim finds that he needs the money and sells the note to a third party for $\\\\$6{,}709.00$. What annual exact simple interest rate will the third party receive for the investment? [ANS] $\\%$ (Note: Your answer should be correct to two decimal places to be counted as correct.)", "answer_v1": [ "17.4314" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "After buying a new car, Jim decides to sell his old car to a friend Mark. Jim accepts a $130$ day note for $\\\\$6{,}693.17$ at $7.2 \\%$ exact simple interest as payment (both principal and interest will be paid at the end of $130$ days). $105$ days later, Jim finds that he needs the money and sells the note to a third party for $\\\\$6{,}703.00$. What annual exact simple interest rate will the third party receive for the investment? [ANS] $\\%$ (Note: Your answer should be correct to two decimal places to be counted as correct.)", "answer_v2": [ "35.244" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "After buying a new car, Jim decides to sell his old car to a friend Mark. Jim accepts a $137$ day note for $\\\\$6{,}660.54$ at $7.4 \\%$ exact simple interest as payment (both principal and interest will be paid at the end of $137$ days). $93$ days later, Jim finds that he needs the money and sells the note to a third party for $\\\\$6{,}705.00$. What annual exact simple interest rate will the third party receive for the investment? [ANS] $\\%$ (Note: Your answer should be correct to two decimal places to be counted as correct.)", "answer_v3": [ "17.3875" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0183", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "2", "keywords": [ "financial mathematics", "unknown time and logarithms" ], "problem_v1": "How long will it take for an investment of 1800 dollars to grow to 6200 dollars, if the effective rate of interest is 8.2 percent? (Assume compound interest at all times.)\nAnswer=[ANS] years. (Be sure to give several decimal places of accuracy.)", "answer_v1": [ "15.6927306568771" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "How long will it take for an investment of 1000 dollars to grow to 6900 dollars, if the effective rate of interest is 6.5 percent? (Assume compound interest at all times.)\nAnswer=[ANS] years. (Be sure to give several decimal places of accuracy.)", "answer_v2": [ "30.6713389693108" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "How long will it take for an investment of 1300 dollars to grow to 6200 dollars, if the effective rate of interest is 7 percent? (Assume compound interest at all times.)\nAnswer=[ANS] years. (Be sure to give several decimal places of accuracy.)", "answer_v3": [ "23.0892142072295" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0184", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "5", "keywords": [ "financial mathematics", "unknown time and logarithms" ], "problem_v1": "Xena invests 4600 dollars in an account paying 11.3 percent interest convertible monthly. How long will it take for her account balance to reach 9200 dollars? (Assume compound interest at all times.) Answer=[ANS] years. (Be sure to give several decimal places of accuracy.)", "answer_v1": [ "6.16288186300546" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Xena invests 3000 dollars in an account paying 10.3 percent interest convertible monthly. How long will it take for her account balance to reach 10000 dollars? (Assume compound interest at all times.) Answer=[ANS] years. (Be sure to give several decimal places of accuracy.)", "answer_v2": [ "11.7391504279354" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Xena invests 3600 dollars in an account paying 10.5 percent interest convertible monthly. How long will it take for her account balance to reach 9200 dollars? (Assume compound interest at all times.) Answer=[ANS] years. (Be sure to give several decimal places of accuracy.)", "answer_v3": [ "8.97493912335303" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0185", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "4", "keywords": [ "financial mathematics", "unknown time and logarithms" ], "problem_v1": "Your cousin Ray borrows 1600 dollars now, repays 800 dollars in two years, and then borrows 1150 dollars in another three years, all at nominal rates of interest of 11.1 percent convertible quarterly. Your other cousin Jay borrows 1950 dollars $t$ years from now at the same interest rate. If the present value of both of your cousin's debts is the same, what is $t$? (Assume compound interest at all times.)\nAnswer=[ANS] years. (Be sure to give several decimal places of accuracy.)", "answer_v1": [ "1.6791688863482" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Your cousin Ray borrows 1300 dollars now, repays 900 dollars in two years, and then borrows 1000 dollars in another three years, all at nominal rates of interest of 8.9 percent convertible quarterly. Your other cousin Jay borrows 1400 dollars $t$ years from now at the same interest rate. If the present value of both of your cousin's debts is the same, what is $t$? (Assume compound interest at all times.)\nAnswer=[ANS] years. (Be sure to give several decimal places of accuracy.)", "answer_v2": [ "1.85356654973819" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Your cousin Ray borrows 1400 dollars now, repays 850 dollars in two years, and then borrows 1050 dollars in another three years, all at nominal rates of interest of 10.1 percent convertible quarterly. Your other cousin Jay borrows 1600 dollars $t$ years from now at the same interest rate. If the present value of both of your cousin's debts is the same, what is $t$? (Assume compound interest at all times.)\nAnswer=[ANS] years. (Be sure to give several decimal places of accuracy.)", "answer_v3": [ "1.76744886683756" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0186", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "5", "keywords": [ "financial mathematics", "unknown time and logarithms" ], "problem_v1": "Melissa deposits 4600 dollars in an account paying 11.5 percent interest convertible monthly. One year later, she withdraws 400 dollars. If there are no other transactions, how long will it take (since her original deposit) for her account balance to reach 9200 dollars? (Assume simple interest between compoundings, use the monthly interest rate in the simple interest formula, and assume that a month has 365/12 days.) Answer=[ANS] months and [ANS] days. (Note: your answer for the number of months should be a whole number, while your answer for the number of days should be a decimal approximation.)", "answer_v1": [ "81", "4.18593935644421" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Melissa deposits 3000 dollars in an account paying 10.7 percent interest convertible monthly. One year later, she withdraws 500 dollars. If there are no other transactions, how long will it take (since her original deposit) for her account balance to reach 8200 dollars? (Assume simple interest between compoundings, use the monthly interest rate in the simple interest formula, and assume that a month has 365/12 days.) Answer=[ANS] months and [ANS] days. (Note: your answer for the number of months should be a whole number, while your answer for the number of days should be a decimal approximation.)", "answer_v2": [ "131", "16.8551174455449" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Melissa deposits 3600 dollars in an account paying 11.1 percent interest convertible monthly. One year later, she withdraws 400 dollars. If there are no other transactions, how long will it take (since her original deposit) for her account balance to reach 8600 dollars? (Assume simple interest between compoundings, use the monthly interest rate in the simple interest formula, and assume that a month has 365/12 days.) Answer=[ANS] months and [ANS] days. (Note: your answer for the number of months should be a whole number, while your answer for the number of days should be a decimal approximation.)", "answer_v3": [ "105", "29.1810689538952" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0187", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "3", "keywords": [ "financial mathematics", "effective and nominal rates" ], "problem_v1": "You deposit 1670 dollars into an account paying a nominal rate of interest of 10 percent convertible semiannually. At the same time, your friend deposits 1550 dollars into an account paying a nominal rate of interest of 10 percent convertible quarterly. How many years will it take for your account balances to be equal? (Assume compound interest at all times.)\nAnswer=[ANS] years. (Be sure to give several decimal places of accuracy!)", "answer_v1": [ "62.6563445429366" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "You deposit 1450 dollars into an account paying a nominal rate of interest of 9.2 percent convertible semiannually. At the same time, your friend deposits 1300 dollars into an account paying a nominal rate of interest of 9.2 percent convertible quarterly. How many years will it take for your account balances to be equal? (Assume compound interest at all times.)\nAnswer=[ANS] years. (Be sure to give several decimal places of accuracy!)", "answer_v2": [ "107.988034191139" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "You deposit 1520 dollars into an account paying a nominal rate of interest of 9.4 percent convertible semiannually. At the same time, your friend deposits 1400 dollars into an account paying a nominal rate of interest of 9.4 percent convertible quarterly. How many years will it take for your account balances to be equal? (Assume compound interest at all times.)\nAnswer=[ANS] years. (Be sure to give several decimal places of accuracy!)", "answer_v3": [ "77.9773606638522" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0188", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "5", "keywords": [ "exponential functions", "compound interest", "effective rate", "nominal rate", "continuous exponential growth" ], "problem_v1": "If you need \\$50,000 seven years from now, what is the minimum amount of money you need to deposit into a bank account that pays 5\\% annual interest, compounded (give your answers to the nearest cent) (give your answers to the nearest cent):\n(a) annually? \\$ [ANS]\n(b) monthly? \\$ [ANS]\n(c) daily (assuming 365 days in a year)? \\$ [ANS]", "answer_v1": [ "35534.1", "35260", "35235.2" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "If you need \\$20,000 four years from now, what is the minimum amount of money you need to deposit into a bank account that pays 7\\% annual interest, compounded (give your answers to the nearest cent) (give your answers to the nearest cent):\n(a) annually? \\$ [ANS]\n(b) monthly? \\$ [ANS]\n(c) daily (assuming 365 days in a year)? \\$ [ANS]", "answer_v2": [ "15257.9", "15128", "15116.1" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "If you need \\$30,000 five years from now, what is the minimum amount of money you need to deposit into a bank account that pays 6\\% annual interest, compounded (give your answers to the nearest cent) (give your answers to the nearest cent):\n(a) annually? \\$ [ANS]\n(b) monthly? \\$ [ANS]\n(c) daily (assuming 365 days in a year)? \\$ [ANS]", "answer_v3": [ "22417.8", "22241.2", "22225.1" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Financial_mathematics_0189", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "5", "keywords": [ "exponential functions", "compound interest", "effective rate", "nominal rate", "continuous exponential growth" ], "problem_v1": "An investment grows by 7\\% per year for 15 years. By what percent does it increase over the 15-year period? [ANS] \\%", "answer_v1": [ "175.9" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "An investment grows by 3\\% per year for 20 years. By what percent does it increase over the 20-year period? [ANS] \\%", "answer_v2": [ "80.611" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "An investment grows by 4\\% per year for 15 years. By what percent does it increase over the 15-year period? [ANS] \\%", "answer_v3": [ "80.09" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0190", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "4", "keywords": [ "exponential functions", "growth rate", "growth factor" ], "problem_v1": "(a) The annual inflation rate is $3.5$ \\% per year. If a movie ticket costs \\$11.00 today, find a formula for $p$, the price of a movie ticket $t$ years from today, assuming that movie tickets keep up with inflation. $P=f(t)=$ [ANS]\n(b) According to your formula, how much will a movie ticket cost in $25$ years? [ANS]", "answer_v1": [ "11*1.035^t", "25.9957" ], "answer_type_v1": [ "EX", "NV" ], "options_v1": [ [], [] ], "problem_v2": "(a) The annual inflation rate is $3.8$ \\% per year. If a movie ticket costs \\$8.00 today, find a formula for $p$, the price of a movie ticket $t$ years from today, assuming that movie tickets keep up with inflation. $P=f(t)=$ [ANS]\n(b) According to your formula, how much will a movie ticket cost in $15$ years? [ANS]", "answer_v2": [ "8*1.038^t", "13.9975" ], "answer_type_v2": [ "EX", "NV" ], "options_v2": [ [], [] ], "problem_v3": "(a) The annual inflation rate is $3.5$ \\% per year. If a movie ticket costs \\$9.00 today, find a formula for $p$, the price of a movie ticket $t$ years from today, assuming that movie tickets keep up with inflation. $P=f(t)=$ [ANS]\n(b) According to your formula, how much will a movie ticket cost in $20$ years? [ANS]", "answer_v3": [ "9*1.035^t", "17.9081" ], "answer_type_v3": [ "EX", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0191", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "2", "keywords": [ "exponential functions", "growth rate", "growth factor" ], "problem_v1": "The value $V$ (in dollars) of an investment in year $t$ is given by $ V=2700 (1.035)^t$. Select all of the following which correctly describe the investment (more than one may be correct). [ANS] A. An initial investment of \\$2700 increases by 0.35\\% per year. B. An initial investment of \\$2700 increases by 0.035\\% every year. C. An initial investment of \\$2700 increases by 3.5\\% per year. D. An initial investment of \\$2700 increases by 94.5 dollars every year. E. An initial investment of \\$2700 increases by 1.035\\% per year. F. None of the above", "answer_v1": [ "C" ], "answer_type_v1": [ "MCS" ], "options_v1": [ [ "A", "B", "C", "D", "E", "F" ] ], "problem_v2": "The value $V$ (in dollars) of an investment in year $t$ is given by $ V=1600 (1.0425)^t$. Select all of the following which correctly describe the investment (more than one may be correct). [ANS] A. An initial investment of \\$1600 increases by 0.0425\\% every year. B. An initial investment of \\$1600 increases by 1.0425\\% per year. C. An initial investment of \\$1600 increases by 68 dollars every year. D. An initial investment of \\$1600 increases by 4.25\\% per year. E. An initial investment of \\$1600 increases by 0.425\\% per year. F. None of the above", "answer_v2": [ "D" ], "answer_type_v2": [ "MCS" ], "options_v2": [ [ "A", "B", "C", "D", "E", "F" ] ], "problem_v3": "The value $V$ (in dollars) of an investment in year $t$ is given by $ V=2000 (1.035)^t$. Select all of the following which correctly describe the investment (more than one may be correct). [ANS] A. An initial investment of \\$2000 increases by 0.035\\% every year. B. An initial investment of \\$2000 increases by 3.5\\% per year. C. An initial investment of \\$2000 increases by 0.35\\% per year. D. An initial investment of \\$2000 increases by 70 dollars every year. E. An initial investment of \\$2000 increases by 1.035\\% per year. F. None of the above", "answer_v3": [ "B" ], "answer_type_v3": [ "MCS" ], "options_v3": [ [ "A", "B", "C", "D", "E", "F" ] ] }, { "id": "Financial_mathematics_0192", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "3", "keywords": [ "algebra", "natural exponential function" ], "problem_v1": "If \\$38900 is invested at an interest rate of 8 percent per year, find the value of the investment at the end of 5 years for the following compounding methods. Round answers to the nearest cent. Compounded\n(a) annually: \u00a0 \\$ [ANS]\n(b) semiannually: \u00a0 \\$ [ANS]\n(c) monthly: \u00a0 \\$ [ANS]\n(d) daily: \u00a0 \\$ [ANS]\n(e) continuously: \u00a0 \\$ [ANS]", "answer_v1": [ "57156.86", "57581.50", "57955.00", "58029.44", "58031.98" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [] ], "problem_v2": "If \\$8700 is invested at an interest rate of 10 percent per year, find the value of the investment at the end of 5 years for the following compounding methods. Round answers to the nearest cent. Compounded\n(a) annually: \u00a0 \\$ [ANS]\n(b) semiannually: \u00a0 \\$ [ANS]\n(c) monthly: \u00a0 \\$ [ANS]\n(d) daily: \u00a0 \\$ [ANS]\n(e) continuously: \u00a0 \\$ [ANS]", "answer_v2": [ "14011.44", "14171.38", "14314.19", "14342.89", "14343.88" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [] ], "problem_v3": "If \\$19100 is invested at an interest rate of 8 percent per year, find the value of the investment at the end of 5 years for the following compounding methods. Round answers to the nearest cent. Compounded\n(a) annually: \u00a0 \\$ [ANS]\n(b) semiannually: \u00a0 \\$ [ANS]\n(c) monthly: \u00a0 \\$ [ANS]\n(d) daily: \u00a0 \\$ [ANS]\n(e) continuously: \u00a0 \\$ [ANS]", "answer_v3": [ "28064.17", "28272.67", "28456.05", "28492.60", "28493.85" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [] ] }, { "id": "Financial_mathematics_0193", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "4", "keywords": [ "continuous compounding" ], "problem_v1": "Complete the table below giving the amount $P$ that must be invested at interest rate 9 \\% compounded continuously to obtain a balance of $A$=\\$170000 in $t$ years.\n$\\begin{array}{cc}\\hline t & P \\\\\\hline1 & [ANS] \\\\\\hline10 & [ANS] \\\\\\hline20 & [ANS] \\\\\\hline30 & [ANS] \\\\\\hline40 & [ANS] \\\\\\hline50 & [ANS] \\\\\\hline\\end{array}$", "answer_v1": [ "170000 /(e^{0.09*1})", "170000 /(e^{0.09*10})", "170000 /(e^{0.09*20})", "170000 /(e^{0.09*30})", "170000 /(e^{0.09*40})", "170000 /(e^{0.09*50})" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [], [] ], "problem_v2": "Complete the table below giving the amount $P$ that must be invested at interest rate 11.5 \\% compounded continuously to obtain a balance of $A$=\\$60000 in $t$ years.\n$\\begin{array}{cc}\\hline t & P \\\\\\hline1 & [ANS] \\\\\\hline10 & [ANS] \\\\\\hline20 & [ANS] \\\\\\hline30 & [ANS] \\\\\\hline40 & [ANS] \\\\\\hline50 & [ANS] \\\\\\hline\\end{array}$", "answer_v2": [ "60000 /(e^{0.115*1})", "60000 /(e^{0.115*10})", "60000 /(e^{0.115*20})", "60000 /(e^{0.115*30})", "60000 /(e^{0.115*40})", "60000 /(e^{0.115*50})" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [], [] ], "problem_v3": "Complete the table below giving the amount $P$ that must be invested at interest rate 9.5 \\% compounded continuously to obtain a balance of $A$=\\$100000 in $t$ years.\n$\\begin{array}{cc}\\hline t & P \\\\\\hline1 & [ANS] \\\\\\hline10 & [ANS] \\\\\\hline20 & [ANS] \\\\\\hline30 & [ANS] \\\\\\hline40 & [ANS] \\\\\\hline50 & [ANS] \\\\\\hline\\end{array}$", "answer_v3": [ "100000 /(e^{0.095*1})", "100000 /(e^{0.095*10})", "100000 /(e^{0.095*20})", "100000 /(e^{0.095*30})", "100000 /(e^{0.095*40})", "100000 /(e^{0.095*50})" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [], [] ] }, { "id": "Financial_mathematics_0194", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "4", "keywords": [ "algebra", "solve for variable' 'fraction", "Exponential", "Logarithmic", "Applications" ], "problem_v1": "The rule of 72 states that if an investment earns $P$ \\% interest per year, it will take approximately $72/P$ years for your money to double.\nYou invest 7774 at 3.3 \\% interest annually.\nAccording to the rule of 72, what is the doubling time, in years, for this investment [ANS]\nUse the doubling time to find a formula for $V(t)$, the value of your investment at time $t$. $V(t)=$ [ANS]\nAccording to the doubling time, how much will your investment be worth after 36 years? [ANS]\nUse the compound interest formula to find how much the investment will be worth after 36 years. [ANS].\nYou may notice that your two values for the investment's worth after 36 years are different. That is because the doubling time you found with the rule of 72 is only an approximation. If the approximation were better, the two values would be the same.", "answer_v1": [ "21.8181818181818", "7774*2**(t/21.8181818181818)", "24397.4271", "25018.20293652" ], "answer_type_v1": [ "NV", "EX", "NV", "NV" ], "options_v1": [ [], [], [], [] ], "problem_v2": "The rule of 72 states that if an investment earns $P$ \\% interest per year, it will take approximately $72/P$ years for your money to double.\nYou invest 1747 at 4.8 \\% interest annually.\nAccording to the rule of 72, what is the doubling time, in years, for this investment [ANS]\nUse the doubling time to find a formula for $V(t)$, the value of your investment at time $t$. $V(t)=$ [ANS]\nAccording to the doubling time, how much will your investment be worth after 17 years? [ANS]\nUse the compound interest formula to find how much the investment will be worth after 17 years. [ANS].\nYou may notice that your two values for the investment's worth after 17 years are different. That is because the doubling time you found with the rule of 72 is only an approximation. If the approximation were better, the two values would be the same.", "answer_v2": [ "15", "1747*2**(t/15)", "3832.30639050794", "3876.45467140272" ], "answer_type_v2": [ "NV", "EX", "NV", "NV" ], "options_v2": [ [], [], [], [] ], "problem_v3": "The rule of 72 states that if an investment earns $P$ \\% interest per year, it will take approximately $72/P$ years for your money to double.\nYou invest 3821 at 3.4 \\% interest annually.\nAccording to the rule of 72, what is the doubling time, in years, for this investment [ANS]\nUse the doubling time to find a formula for $V(t)$, the value of your investment at time $t$. $V(t)=$ [ANS]\nAccording to the doubling time, how much will your investment be worth after 22 years? [ANS]\nUse the compound interest formula to find how much the investment will be worth after 22 years. [ANS].\nYou may notice that your two values for the investment's worth after 22 years are different. That is because the doubling time you found with the rule of 72 is only an approximation. If the approximation were better, the two values would be the same.", "answer_v3": [ "21.1764705882353", "3821*2**(t/21.1764705882353)", "7850.79708831197", "7973.13082876767" ], "answer_type_v3": [ "NV", "EX", "NV", "NV" ], "options_v3": [ [], [], [], [] ] }, { "id": "Financial_mathematics_0195", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "3", "keywords": [ "algebra", "logarithmic equation" ], "problem_v1": "Find the time required for an investment of 1 dollars to grow to 8300 dollars at an interest rate of 7.5 percent per year, compounded quarterly. Your answer is $t=$ [ANS] years.", "answer_v1": [ "121.444652921773" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Find the time required for an investment of 1 dollars to grow to 6200 dollars at an interest rate of 7.5 percent per year, compounded quarterly. Your answer is $t=$ [ANS] years.", "answer_v2": [ "117.518886232577" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Find the time required for an investment of 1 dollars to grow to 6900 dollars at an interest rate of 7.5 percent per year, compounded quarterly. Your answer is $t=$ [ANS] years.", "answer_v3": [ "118.958511276052" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0196", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "3", "keywords": [ "algebra", "natural exponential function" ], "problem_v1": "If 7600 dollars is invested at an interest rate of 8 percent per year, compounded semiannually, find the value of the investment after the given number of years.\n(a) 5 years: Your answer is [ANS]\n(b) 10 years: Your answer is [ANS]\n(c) 15 years: Your answer is [ANS]", "answer_v1": [ "11249.8565653794", "16652.535887054", "24649.8210762093" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "If 900 dollars is invested at an interest rate of 10 percent per year, compounded semiannually, find the value of the investment after the given number of years.\n(a) 5 years: Your answer is [ANS]\n(b) 10 years: Your answer is [ANS]\n(c) 15 years: Your answer is [ANS]", "answer_v2": [ "1466.0051640997", "2387.96793463", "3889.7481376356" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "If 3200 dollars is invested at an interest rate of 8 percent per year, compounded semiannually, find the value of the investment after the given number of years.\n(a) 5 years: Your answer is [ANS]\n(b) 10 years: Your answer is [ANS]\n(c) 15 years: Your answer is [ANS]", "answer_v3": [ "4736.7817117387", "7011.59405770694", "10378.8720320881" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Financial_mathematics_0197", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "5", "keywords": [ "calculus", "logarithmic functions", "logarithms", "laws of logarithms" ], "problem_v1": "What is the doubling time of prices which are increasing by 8 percent per year? doubling time=[ANS] yr", "answer_v1": [ "9.00647" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "What is the doubling time of prices which are increasing by 2 percent per year? doubling time=[ANS] yr", "answer_v2": [ "35.0028" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "What is the doubling time of prices which are increasing by 4 percent per year? doubling time=[ANS] yr", "answer_v3": [ "17.673" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0198", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "2", "keywords": [], "problem_v1": "If your money earns $p$ percent interest per year then at the end of the year your money is multiplied with the factor $\\left(1+\\frac{p}{100}\\right)$. (The interest is paid annually---at this stage we ignore subtleties like paying interest every month.) You invest \\$ 600 at 8 \\% annual interest. After ten years you have \\$ [ANS] in the Bank.", "answer_v1": [ "1295.35499836367" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "If your money earns $p$ percent interest per year then at the end of the year your money is multiplied with the factor $\\left(1+\\frac{p}{100}\\right)$. (The interest is paid annually---at this stage we ignore subtleties like paying interest every month.) You invest \\$ 1000 at 3 \\% annual interest. After ten years you have \\$ [ANS] in the Bank.", "answer_v2": [ "1343.91637934412" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "If your money earns $p$ percent interest per year then at the end of the year your money is multiplied with the factor $\\left(1+\\frac{p}{100}\\right)$. (The interest is paid annually---at this stage we ignore subtleties like paying interest every month.) You invest \\$ 700 at 5 \\% annual interest. After ten years you have \\$ [ANS] in the Bank.", "answer_v3": [ "1140.22623874421" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0199", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "4", "keywords": [ "algebra" ], "problem_v1": "You have \\$6500. The best interest rate you can find is $2.5\\%$ compounded quarterly. For how long should you deposit the money in order to have \\$9600? [ANS] years", "answer_v1": [ "15.6471313599728" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "You have \\$5100. The best interest rate you can find is $1\\%$ compounded quarterly. For how long should you deposit the money in order to have \\$10000? [ANS] years", "answer_v2": [ "67.4185883692754" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "You have \\$5600. The best interest rate you can find is $1.5\\%$ compounded quarterly. For how long should you deposit the money in order to have \\$9600? [ANS] years", "answer_v3": [ "36.0004325811041" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0200", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "4", "keywords": [ "algebra" ], "problem_v1": "How long will it take for \\$4500 compounded semiannually at an annual rate of $2.5\\%$ to amount to \\$6600? [ANS] years", "answer_v1": [ "15.4152399151135" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "How long will it take for \\$3100 compounded semiannually at an annual rate of $1\\%$ to amount to \\$7000? [ANS] years", "answer_v2": [ "81.6542614995239" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "How long will it take for \\$3600 compounded semiannually at an annual rate of $1.5\\%$ to amount to \\$6600? [ANS] years", "answer_v3": [ "40.5603988117673" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0201", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "2", "keywords": [ "exponential functions", "growth rate", "growth factor" ], "problem_v1": "Let $A=f(t)$ be the amount of money in an account, in dollars, $t$ months after an initial investment of \\$ $7000$.\n(a) Find a formula for $A$ given that it grows by $4$ \\% each month. $A=f(t)=$ [ANS]\n(b) Find a formula for $A$ given that it grows by $28$ \\% every $7$ months. $A=f(t)=$ [ANS]\n(c) Which scenario has the largest monthly percent growth rate? [ANS] A. Earning $4$ \\% every month. B. Earning $28$ \\% every $7$ months. C. They have the same monthly percent growth rate.", "answer_v1": [ "7000*1.04^t", "7000*1.03589^t", "A" ], "answer_type_v1": [ "EX", "EX", "MCS" ], "options_v1": [ [], [], [ "A", "B", "C" ] ], "problem_v2": "Let $A=f(t)$ be the amount of money in an account, in dollars, $t$ months after an initial investment of \\$ $1500$.\n(a) Find a formula for $A$ given that it grows by $6$ \\% each month. $A=f(t)=$ [ANS]\n(b) Find a formula for $A$ given that it grows by $24$ \\% every $4$ months. $A=f(t)=$ [ANS]\n(c) Which scenario has the largest monthly percent growth rate? [ANS] A. Earning $6$ \\% every month. B. Earning $24$ \\% every $4$ months. C. They have the same monthly percent growth rate.", "answer_v2": [ "1500*1.06^t", "1500*1.05525^t", "A" ], "answer_type_v2": [ "EX", "EX", "MCS" ], "options_v2": [ [], [], [ "A", "B", "C" ] ], "problem_v3": "Let $A=f(t)$ be the amount of money in an account, in dollars, $t$ months after an initial investment of \\$ $3500$.\n(a) Find a formula for $A$ given that it grows by $4$ \\% each month. $A=f(t)=$ [ANS]\n(b) Find a formula for $A$ given that it grows by $20$ \\% every $5$ months. $A=f(t)=$ [ANS]\n(c) Which scenario has the largest monthly percent growth rate? [ANS] A. Earning $20$ \\% every $5$ months. B. Earning $4$ \\% every month. C. They have the same monthly percent growth rate.", "answer_v3": [ "3500*1.04^t", "3500*1.03714^t", "B" ], "answer_type_v3": [ "EX", "EX", "MCS" ], "options_v3": [ [], [], [ "A", "B", "C" ] ] }, { "id": "Financial_mathematics_0202", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "4", "keywords": [ "exponents" ], "problem_v1": "The value of an investment increases by $0.08$ \\% each day. By what percent does it increase in a year?\nAnnual growth rate $=$ [ANS] \\%", "answer_v1": [ "33.8947" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "The value of an investment increases by $0.03$ \\% each day. By what percent does it increase in a year?\nAnnual growth rate $=$ [ANS] \\%", "answer_v2": [ "11.5702" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "The value of an investment increases by $0.05$ \\% each day. By what percent does it increase in a year?\nAnnual growth rate $=$ [ANS] \\%", "answer_v3": [ "20.0159" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0203", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "2", "keywords": [ "exponential functions", "growth rate", "growth factor" ], "problem_v1": "Find a formula for the value, $V$, of an investment, in dollars, initially worth \\$ $17000$ that grows by $12$ \\% every $7$ years.\n$V=f(t)=$ [ANS]", "answer_v1": [ "17000*1.12^(t/7)" ], "answer_type_v1": [ "EX" ], "options_v1": [ [] ], "problem_v2": "Find a formula for the value, $V$, of an investment, in dollars, initially worth \\$ $11000$ that grows by $15$ \\% every $4$ years.\n$V=f(t)=$ [ANS]", "answer_v2": [ "11000*1.15^(t/4)" ], "answer_type_v2": [ "EX" ], "options_v2": [ [] ], "problem_v3": "Find a formula for the value, $V$, of an investment, in dollars, initially worth \\$ $13000$ that grows by $12$ \\% every $5$ years.\n$V=f(t)=$ [ANS]", "answer_v3": [ "13000*1.12^(t/5)" ], "answer_type_v3": [ "EX" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0204", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "5", "keywords": [ "exponential functions", "annual growth rate", "linear growth" ], "problem_v1": "An investment is worth 4700 dollars at time $t=0$, with $t$ measured in years.\n(a) If the investment's value grows by 110 dollars per year, find a formula for the value, $V$, at time $t$. $V=$ [ANS]\n(b) If the investment's value grows by 11\\% per year, find a formula for the value, $V$, at time $t$. $V=$ [ANS]", "answer_v1": [ "4700+110*t", "4700*1.11^t" ], "answer_type_v1": [ "EX", "EX" ], "options_v1": [ [], [] ], "problem_v2": "An investment is worth 3600 dollars at time $t=0$, with $t$ measured in years.\n(a) If the investment's value grows by 150 dollars per year, find a formula for the value, $V$, at time $t$. $V=$ [ANS]\n(b) If the investment's value grows by 15\\% per year, find a formula for the value, $V$, at time $t$. $V=$ [ANS]", "answer_v2": [ "3600+150*t", "3600*1.15^t" ], "answer_type_v2": [ "EX", "EX" ], "options_v2": [ [], [] ], "problem_v3": "An investment is worth 4000 dollars at time $t=0$, with $t$ measured in years.\n(a) If the investment's value grows by 110 dollars per year, find a formula for the value, $V$, at time $t$. $V=$ [ANS]\n(b) If the investment's value grows by 11\\% per year, find a formula for the value, $V$, at time $t$. $V=$ [ANS]", "answer_v3": [ "4000+110*t", "4000*1.11^t" ], "answer_type_v3": [ "EX", "EX" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0205", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "2", "keywords": [ "exponential functions", "growth rate", "growth factor" ], "problem_v1": "The balance in an account, $B$, starts at $1750$ dollars and increases $n$ years in a row by a factor of $1.15$ each year. Write a formula for $B=f(n)$. $B=f(n)=$ [ANS]", "answer_v1": [ "1750*1.15^n" ], "answer_type_v1": [ "EX" ], "options_v1": [ [] ], "problem_v2": "The balance in an account, $B$, starts at $1050$ dollars and increases $n$ years in a row by a factor of $1.17$ each year. Write a formula for $B=f(n)$. $B=f(n)=$ [ANS]", "answer_v2": [ "1050*1.17^n" ], "answer_type_v2": [ "EX" ], "options_v2": [ [] ], "problem_v3": "The balance in an account, $B$, starts at $1300$ dollars and increases $n$ years in a row by a factor of $1.15$ each year. Write a formula for $B=f(n)$. $B=f(n)=$ [ANS]", "answer_v3": [ "1300*1.15^n" ], "answer_type_v3": [ "EX" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0206", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "3", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "How many years will it take for an initial investment of \\$22000 to grow to \\$45700? Assume a rate of interest of 11\\% compounded daily. Answer=[ANS] years", "answer_v1": [ "6.6469636191776" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "How many years will it take for an initial investment of \\$11000 to grow to \\$24400? Assume a rate of interest of 4\\% compounded daily. Answer=[ANS] years", "answer_v2": [ "19.9182878208333" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "How many years will it take for an initial investment of \\$15000 to grow to \\$31700? Assume a rate of interest of 6\\% compounded daily. Answer=[ANS] years", "answer_v3": [ "12.4721329908452" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0207", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "2", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "What annual rate of interest compounded annually is required to double an investment in 13 years? Rate=[ANS] \\%", "answer_v1": [ "5.47660764816467" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "What annual rate of interest compounded annually is required to double an investment in 5 years? Rate=[ANS] \\%", "answer_v2": [ "14.8698354997035" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "What annual rate of interest compounded annually is required to double an investment in 8 years? Rate=[ANS] \\%", "answer_v3": [ "9.05077326652577" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0208", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "3", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "Find the principal needed to get \\$1600 in 6 years at 11\\% compounded monthly. Principal=\\$ [ANS]", "answer_v1": [ "829.452254237101" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Find the principal needed to get \\$500 in 9 years at 5\\% compounded monthly. Principal=\\$ [ANS]", "answer_v2": [ "319.112275720284" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Find the principal needed to get \\$900 in 6 years at 7\\% compounded monthly. Principal=\\$ [ANS]", "answer_v3": [ "592.064167572956" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0209", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "3", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "A mutual fund pays 11\\% compounded monthly. How much should I invest now so that 5 years from now I will have \\$4800 in the account?\nAmount=\\$ [ANS]", "answer_v1": [ "2776.30651133075" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A mutual fund pays 4\\% compounded monthly. How much should I invest now so that 7 years from now I will have \\$2700 in the account?\nAmount=\\$ [ANS]", "answer_v2": [ "2041.56649977738" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A mutual fund pays 6\\% compounded monthly. How much should I invest now so that 5 years from now I will have \\$3400 in the account?\nAmount=\\$ [ANS]", "answer_v3": [ "2520.66546723077" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0210", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "3", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "Jim borrows \\$800 at 12\\% per annum compounded quarterly for 5 years. Determine the interest due on the loan.\nInterest due=\\$ [ANS]", "answer_v1": [ "644.888987735532" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Jim borrows \\$100 at 5\\% per annum compounded quarterly for 7 years. Determine the interest due on the loan.\nInterest due=\\$ [ANS]", "answer_v2": [ "41.5992303619225" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Jim borrows \\$400 at 7\\% per annum compounded quarterly for 5 years. Determine the interest due on the loan.\nInterest due=\\$ [ANS]", "answer_v3": [ "165.91127830232" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0211", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "3", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "If \\$800 is invested at 14\\% compounded quarterly, what is the interest earned after: a) 5 years Interest earned=\\$ [ANS]\nb) 6 years Interest earned=\\$ [ANS]", "answer_v1": [ "791.831090772674", "1026.66278977163" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "If \\$100 is invested at 8\\% compounded quarterly, what is the interest earned after: a) 7 years Interest earned=\\$ [ANS]\nb) 3 years Interest earned=\\$ [ANS]", "answer_v2": [ "74.1024206173928", "26.8241794562546" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "If \\$400 is invested at 11\\% compounded quarterly, what is the interest earned after: a) 5 years Interest earned=\\$ [ANS]\nb) 4 years Interest earned=\\$ [ANS]", "answer_v3": [ "288.171372514379", "217.403774333301" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0212", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "3", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "If a bank pays 14\\% compounded monthly, how much should be deposited now to have \\$1800: a) 5 years later Answer=\\$ [ANS]\nb) 6 years later Answer=\\$ [ANS]", "answer_v1": [ "897.482654113957", "780.866470821624" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "If a bank pays 8\\% compounded monthly, how much should be deposited now to have \\$1000: a) 7 years later Answer=\\$ [ANS]\nb) 3 years later Answer=\\$ [ANS]", "answer_v2": [ "572.27159241921", "787.25462993237" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "If a bank pays 11\\% compounded monthly, how much should be deposited now to have \\$1300: a) 5 years later Answer=\\$ [ANS]\nb) 4 years later Answer=\\$ [ANS]", "answer_v3": [ "751.916346818744", "838.927231388767" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0213", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "3", "keywords": [ "percent" ], "problem_v1": "Find the accumulated amount after 5 years if \\$1000 is invested at 12\\% compounded:\na) Annually Accumulated Amount=\\$ [ANS]\nb) Semiannually Accumulated Amount=\\$ [ANS]\nc) Quarterly Accumulated Amount=\\$ [ANS]\nd) Monthly Accumulated Amount=\\$ [ANS]", "answer_v1": [ "1762.3416832", "1790.84769654285", "1806.11123466941", "1816.69669856409" ], "answer_type_v1": [ "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [] ], "problem_v2": "Find the accumulated amount after 7 years if \\$200 is invested at 5\\% compounded:\na) Annually Accumulated Amount=\\$ [ANS]\nb) Semiannually Accumulated Amount=\\$ [ANS]\nc) Quarterly Accumulated Amount=\\$ [ANS]\nd) Monthly Accumulated Amount=\\$ [ANS]", "answer_v2": [ "281.42008453125", "282.594764194753", "283.198460723845", "283.607210445208" ], "answer_type_v2": [ "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [] ], "problem_v3": "Find the accumulated amount after 5 years if \\$500 is invested at 7\\% compounded:\na) Annually Accumulated Amount=\\$ [ANS]\nb) Semiannually Accumulated Amount=\\$ [ANS]\nc) Quarterly Accumulated Amount=\\$ [ANS]\nd) Monthly Accumulated Amount=\\$ [ANS]", "answer_v3": [ "701.27586535", "705.299380310561", "707.3890978779", "708.812629806995" ], "answer_type_v3": [ "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [] ] }, { "id": "Financial_mathematics_0214", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "3", "keywords": [ "percent" ], "problem_v1": "Find the amount accrued if \\$800 is invested at 12\\% compounded monthly for 11 months. Amount=\\$ [ANS]", "answer_v1": [ "892.534677332253" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Find the amount accrued if \\$100 is invested at 5\\% compounded monthly for 17 months. Amount=\\$ [ANS]", "answer_v2": [ "107.324435944722" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Find the amount accrued if \\$400 is invested at 7\\% compounded monthly for 8 months. Amount=\\$ [ANS]", "answer_v3": [ "419.052256646724" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0215", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "3", "keywords": [ "percent" ], "problem_v1": "Suppose \\$800 is invested for 5 years at a nominal yearly interest rate that is compounded semi-annually, further suppose it accumulates to 1432.67 after 5 years. Find the annual nominal interest rate of the investment.\nAnnual nominal interest rate=[ANS] \\%.", "answer_v1": [ "12" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose \\$100 is invested for 7 years at a nominal yearly interest rate that is compounded quarterly, further suppose it accumulates to 141.59 after 7 years. Find the annual nominal interest rate of the investment.\nAnnual nominal interest rate=[ANS] \\%.", "answer_v2": [ "5" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose \\$400 is invested for 5 years at a nominal yearly interest rate that is compounded quarterly, further suppose it accumulates to 565.91 after 5 years. Find the annual nominal interest rate of the investment.\nAnnual nominal interest rate=[ANS] \\%.", "answer_v3": [ "7" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0216", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "5", "keywords": [ "exponential model" ], "problem_v1": "If 5000 dollars invested in a bank account for 8 years, compounded quarterly, amounts to 7382.09 dollars, what is the interest rate paid by the account? [ANS] \\%.\nNOTE: Give your answer to the nearest tenth of a percent.", "answer_v1": [ "4.9" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "If 2000 dollars invested in a bank account for 10 years, compounded quarterly, amounts to 2805.86 dollars, what is the interest rate paid by the account? [ANS] \\%.\nNOTE: Give your answer to the nearest tenth of a percent.", "answer_v2": [ "3.4" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "If 3000 dollars invested in a bank account for 8 years, compounded quarterly, amounts to 4059.98 dollars, what is the interest rate paid by the account? [ANS] \\%.\nNOTE: Give your answer to the nearest tenth of a percent.", "answer_v3": [ "3.8" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0217", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "4", "keywords": [ "exponential model", "CPI" ], "problem_v1": "Ashley bought a house in 1968 for \\$89,926 and sold it in 1996.\n(a) If the 1968 CPI is 34.8 and the 1996 CPI is 156.9 how much would the house be worth in 1996 dollars? Answer: \\$ [ANS]\n(b) To the nearest hundredth, what is the scaling factor for converting 1968 dollars to 1996 dollars? Answer: [ANS]\n(c) If the 2000 CPI is 172.2, how much is the house worth in 2000 dollars? Answer: \\$ [ANS]", "answer_v1": [ "405442.224137931", "4.50862068965517", "444978.655172414" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Gary bought a house in 1961 for \\$65,652 and sold it in 1999.\n(a) If the 1961 CPI is 29.9 and the 1999 CPI is 166.6 how much would the house be worth in 1999 dollars? Answer: \\$ [ANS]\n(b) To the nearest hundredth, what is the scaling factor for converting 1961 dollars to 1999 dollars? Answer: [ANS]\n(c) If the 2001 CPI is 177.7, how much is the house worth in 2001 dollars? Answer: \\$ [ANS]", "answer_v2": [ "365806.795986622", "5.57190635451505", "390179.277591973" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Chris bought a house in 1962 for \\$80,616 and sold it in 1988.\n(a) If the 1962 CPI is 30.9 and the 1988 CPI is 118.3 how much would the house be worth in 1988 dollars? Answer: \\$ [ANS]\n(b) To the nearest hundredth, what is the scaling factor for converting 1962 dollars to 1988 dollars? Answer: [ANS]\n(c) If the 1999 CPI is 166.6, how much is the house worth in 1999 dollars? Answer: \\$ [ANS]", "answer_v3": [ "308636.660194175", "3.82847896440129", "434648.077669903" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Financial_mathematics_0218", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "4", "keywords": [ "exponential model", "inflation" ], "problem_v1": "Products priced at \\$ 202.43 at the beginning of 1986 cost \\$ 257.29 at the beginning of 1998. Assume that the annual inflation rate is unchanged over this time period and into the indefinite future.\n(a) Calculate the average annual inflation rate over this time period. Answer: [ANS] \\% (b) Find the month and year these same products will cost \\$ 492.06. Month: [ANS] Year: [ANS]", "answer_v1": [ "2.01851619399909", "JUNE", "2030" ], "answer_type_v1": [ "NV", "MCS", "NV" ], "options_v1": [ [], [ "January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December" ], [] ], "problem_v2": "Products priced at \\$ 116.60 at the beginning of 1985 cost \\$ 286.34 at the beginning of 2004. Assume that the annual inflation rate is unchanged over this time period and into the indefinite future.\n(a) Calculate the average annual inflation rate over this time period. Answer: [ANS] \\% (b) Find the month and year these same products will cost \\$ 429.91. Month: [ANS] Year: [ANS]", "answer_v2": [ "4.84216295505602", "AUGUST", "2012" ], "answer_type_v2": [ "NV", "MCS", "NV" ], "options_v2": [ [], [ "January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December" ], [] ], "problem_v3": "Products priced at \\$ 162.69 at the beginning of 1985 cost \\$ 221.09 at the beginning of 2000. Assume that the annual inflation rate is unchanged over this time period and into the indefinite future.\n(a) Calculate the average annual inflation rate over this time period. Answer: [ANS] \\% (b) Find the month and year these same products will cost \\$ 455.72. Month: [ANS] Year: [ANS]", "answer_v3": [ "2.06587177731989", "MAY", "2035" ], "answer_type_v3": [ "NV", "MCS", "NV" ], "options_v3": [ [], [ "January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December" ], [] ] }, { "id": "Financial_mathematics_0219", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "3", "keywords": [], "problem_v1": "What nominal annual discount rate compounded quarterly is equivalent to a nominal rate of interest of 16\\% compounded monthly. Nominal discount rate=[ANS] \\%", "answer_v1": [ "15.5826286630705" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "What nominal annual discount rate compounded semiannually is equivalent to a nominal rate of interest of 3\\% compounded monthly. Nominal discount rate=[ANS] \\%", "answer_v2": [ "2.97392402052437" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "What nominal annual discount rate compounded quarterly is equivalent to a nominal rate of interest of 7\\% compounded monthly. Nominal discount rate=[ANS] \\%", "answer_v3": [ "6.91912042377538" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0220", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "5", "keywords": [ "maturity date", "effective annual interest rate" ], "problem_v1": "A \\$ 75.06 loan is issued today. It will be repaid in two \\$ 50 installments. The effective annual rate of interest on the loan is 4 \\%. The first installment is due in 6 years. When is the second installment due? (Round to the nearest integer.)\nThe second installment is due in [ANS] years.", "answer_v1": [ "9" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A \\$ 61.66 loan is issued today. It will be repaid in two \\$ 50 installments. The effective annual rate of interest on the loan is 6 \\%. The first installment is due in 3 years. When is the second installment due? (Round to the nearest integer.)\nThe second installment is due in [ANS] years.", "answer_v2": [ "16" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A \\$ 66.27 loan is issued today. It will be repaid in two \\$ 50 installments. The effective annual rate of interest on the loan is 5 \\%. The first installment is due in 4 years. When is the second installment due? (Round to the nearest integer.)\nThe second installment is due in [ANS] years.", "answer_v3": [ "14" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0221", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "2", "keywords": [ "financial mathematics", "compound interest" ], "problem_v1": "How much do you need to invest in an account earning an annual interest rate of $4.483 \\%$ compounded weekly, so that your money will grow to $\\\\$7{,}510.00$ in $43$ weeks? The amount you need to invest is $[ANS]\n", "answer_v1": [ "7236.81" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "How much do you need to invest in an account earning an annual interest rate of $2.598 \\%$ compounded monthly, so that your money will grow to $\\\\$6{,}160.00$ in $33$ months? The amount you need to invest is $[ANS]\n", "answer_v2": [ "5735.70" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "How much do you need to invest in an account earning an annual interest rate of $3.114 \\%$ compounded daily, so that your money will grow to $\\\\$6{,}630.00$ in $39$ days? The amount you need to invest is $[ANS]\n", "answer_v3": [ "6607.98" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0222", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "2", "keywords": [ "financial mathematics", "compound interest" ], "problem_v1": "In $10$ months, Alex will need $\\\\$1{,}650.00$ to pay her college tuition. How much does she need to invest today into an account earning an interest rate of $7.483 \\%$ compounded monthly, so that she has enough money to pay her tuition? The amount Alex needs to invest is $[ANS]. ", "answer_v1": [ "1550.55" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "In $8$ months, Alex will need $\\\\$1{,}250.00$ to pay his college tuition. How much does he need to invest today into an account earning an interest rate of $5.598 \\%$ compounded monthly, so that he has enough money to pay his tuition? The amount Alex needs to invest is $[ANS].", "answer_v2": [ "1204.31" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "In $9$ months, Alex will need $\\\\$1{,}390.00$ to pay her college tuition. How much does she need to invest today into an account earning an interest rate of $6.114 \\%$ compounded monthly, so that she has enough money to pay her tuition? The amount Alex needs to invest is $[ANS].", "answer_v3": [ "1327.86" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0223", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "2", "keywords": [ "financial mathematics", "compound interest" ], "problem_v1": "John wants to buy a new sports car, and he estimates that he'll need to make a $\\\\$4{,}400.00$ down payment towards his purchase. If he has $27$ months to save up for the new car, how much should he deposit into his account if the account earns $4.327 \\%$ compounded continuously so that he may reach his goal? John needs to deposit $[ANS].", "answer_v1": [ "3991.82" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "John wants to buy a new sports car, and he estimates that he'll need to make a $\\\\$2{,}700.00$ down payment towards his purchase. If he has $15$ months to save up for the new car, how much should he deposit into his account if the account earns $5.727 \\%$ compounded continuously so that he may reach his goal? John needs to deposit $[ANS].", "answer_v2": [ "2513.47" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "John wants to buy a new sports car, and he estimates that he'll need to make a $\\\\$3{,}275.00$ down payment towards his purchase. If he has $18$ months to save up for the new car, how much should he deposit into his account if the account earns $4.422 \\%$ compounded continuously so that he may reach his goal? John needs to deposit $[ANS].", "answer_v3": [ "3064.82" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0224", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "3", "keywords": [ "financial mathematics", "compound interest" ], "problem_v1": "If you make a deposit into a bank account, at what interest rate (compounded weekly) should you invest if you would like to double your investment in $78$ weeks? [ANS] $\\%$ (Note: Your answer should be accurate to two decimal places)", "answer_v1": [ "46.4157" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "If you make a deposit into a bank account, at what interest rate (compounded daily) should you invest if you would like to double your investment in $17$ days? [ANS] $\\%$ (Note: Your answer should be accurate to two decimal places)", "answer_v2": [ "1518.98" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "If you make a deposit into a bank account, at what interest rate (compounded weekly) should you invest if you would like to double your investment in $38$ weeks? [ANS] $\\%$ (Note: Your answer should be accurate to two decimal places)", "answer_v3": [ "95.7221" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0225", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "2", "keywords": [ "financial mathematics", "compound interest" ], "problem_v1": "For how many months do you need to invest your money into a bank account earning an annual interest rate of $10.33 \\%$ compounded monthly if you want to triple your investment? [ANS] months (Note: Your answer should be an integer)", "answer_v1": [ "129" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "For how many months do you need to invest your money into a bank account earning an annual interest rate of $11.73 \\%$ compounded monthly if you want to triple your investment? [ANS] months (Note: Your answer should be an integer)", "answer_v2": [ "113" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "For how many months do you need to invest your money into a bank account earning an annual interest rate of $10.42 \\%$ compounded monthly if you want to triple your investment? [ANS] months (Note: Your answer should be an integer)", "answer_v3": [ "128" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0226", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "3", "keywords": [ "financial mathematics", "compound interest" ], "problem_v1": "Mike and Terri estimate that they want to buy a house for $\\\\$226{,}000.00$, and they need to make a down payment of $15.5 \\%$ of the cost of their house. If they have $30$ months to save for the down payment, how much do they need to invest into an account earning $4.483 \\%$ compounded continuously so that they can reach their goal? Mike and Terri need to invest $[ANS]. ", "answer_v1": [ "31316.02" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Mike and Terri estimate that they want to buy a house for $\\\\$158{,}000.00$, and they need to make a down payment of $17.5 \\%$ of the cost of their house. If they have $21$ months to save for the down payment, how much do they need to invest into an account earning $2.598 \\%$ compounded continuously so that they can reach their goal? Mike and Terri need to invest $[ANS].", "answer_v2": [ "26421.04" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Mike and Terri estimate that they want to buy a house for $\\\\$180{,}000.00$, and they need to make a down payment of $15.5 \\%$ of the cost of their house. If they have $27$ months to save for the down payment, how much do they need to invest into an account earning $3.114 \\%$ compounded continuously so that they can reach their goal? Mike and Terri need to invest $[ANS].", "answer_v3": [ "26012.10" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0227", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "3", "keywords": [ "algebra", "exponents", "exponential functions", "interest", "compounded interest", "compounded quarterly" ], "problem_v1": "Use the formula $A=P \\left(1+\\frac{r}{n}\\right)^{nt}$ to find the total amount of money accumulated for an initial investment $\\\\$1{,}250$ at $11$ \\% compounded quarterly after $11$ years. Amount: $[ANS]", "answer_v1": [ "4123.92" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Use the formula $A=P \\left(1+\\frac{r}{n}\\right)^{nt}$ to find the total amount of money accumulated for an initial investment $\\\\$1{,}000$ at $8$ \\% compounded quarterly after $12$ years. Amount: $[ANS]", "answer_v2": [ "2587.07" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Use the formula $A=P \\left(1+\\frac{r}{n}\\right)^{nt}$ to find the total amount of money accumulated for an initial investment $\\\\$1{,}100$ at $9$ \\% compounded quarterly after $11$ years. Amount: $[ANS]", "answer_v3": [ "2928.05" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0228", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Compound interest", "level": "3", "keywords": [], "problem_v1": "Say you have invested \\$45000 at a yearly interest rate of 14.5\\% compounded weekly. How many years will it take for your investment to double in size? $Years=$ [ANS]", "answer_v1": [ "[log(2)]/[52*log(1+0.145/52)]" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Say you have invested \\$20000 at a yearly interest rate of 7\\% compounded continuously. How many years will it take for your investment to double in size? $Years=$ [ANS]", "answer_v2": [ "[log(2)]/0.07" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Say you have invested \\$30000 at a yearly interest rate of 9\\% compounded weekly. How many years will it take for your investment to double in size? $Years=$ [ANS]", "answer_v3": [ "[log(2)]/[52*log(1+0.09/52)]" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0229", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Continuous interest", "level": "5", "keywords": [ "exponential functions", "growth rate", "growth factor", "continuous exponential growth", "e", "compound interest", "graphs of exponential functions" ], "problem_v1": "An account pays interest at a nominal rate of 11\\% per year. Find the effective annual yield if interest is compounded:\n(a) monthly? [ANS] \\% (b) weekly? [ANS] \\% (c) daily (assuming there are 365 days in the year)? [ANS] \\% (d) continuously? [ANS] \\%", "answer_v1": [ "11.5718836195214", "11.614838619888", "11.6259571637444", "100*(e^0.11-1)" ], "answer_type_v1": [ "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [] ], "problem_v2": "An account pays interest at a nominal rate of 5\\% per year. Find the effective annual yield if interest is compounded:\n(a) monthly? [ANS] \\% (b) weekly? [ANS] \\% (c) daily (assuming there are 365 days in the year)? [ANS] \\% (d) continuously? [ANS] \\%", "answer_v2": [ "5.11618978817332", "5.12458419272003", "5.12674964674626", "100*(e^0.05-1)" ], "answer_type_v2": [ "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [] ], "problem_v3": "An account pays interest at a nominal rate of 7\\% per year. Find the effective annual yield if interest is compounded:\n(a) monthly? [ANS] \\% (b) weekly? [ANS] \\% (c) daily (assuming there are 365 days in the year)? [ANS] \\% (d) continuously? [ANS] \\%", "answer_v3": [ "7.22900808562357", "7.2457696110178", "7.2500983171145", "100*(e^0.07-1)" ], "answer_type_v3": [ "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [] ] }, { "id": "Financial_mathematics_0230", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Continuous interest", "level": "2", "keywords": [ "logarithms", "log", "ln", "half-life", "double-time", "continuous growth rate" ], "problem_v1": "You deposit \\$6000 into an account that earns 7\\% compounded annually. A friend deposits \\$5500 into an account that earns 6.95\\% annual interest, compounded continuously. Will your friend's balance ever equal yours? If so, when? If not, enter NEVER.\nThey will be equal in about [ANS] years (round to nearest whole year).", "answer_v1": [ "47" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "You deposit \\$3000 into an account that earns 5\\% compounded annually. A friend deposits \\$2250 into an account that earns 4.95\\% annual interest, compounded continuously. Will your friend's balance ever equal yours? If so, when? If not, enter NEVER.\nThey will be equal in about [ANS] years (round to nearest whole year).", "answer_v2": [ "405" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "You deposit \\$4000 into an account that earns 7\\% compounded annually. A friend deposits \\$3500 into an account that earns 6.85\\% annual interest, compounded continuously. Will your friend's balance ever equal yours? If so, when? If not, enter NEVER.\nThey will be equal in about [ANS] years (round to nearest whole year).", "answer_v3": [ "159" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0231", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Continuous interest", "level": "3", "keywords": [ "Algebra", "Exponential", "Logarithmic", "Applications" ], "problem_v1": "If 7000 dollars is invested in a bank account at an interest rate of 8 per cent per year, compounded continuously. How many years will it take for your balance to reach 40000 dollars? [ANS]\nNOTE: Give your answer to the nearest tenth of a year.", "answer_v1": [ "21.8" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "If 2000 dollars is invested in a bank account at an interest rate of 10 per cent per year, compounded continuously. How many years will it take for your balance to reach 10000 dollars? [ANS]\nNOTE: Give your answer to the nearest tenth of a year.", "answer_v2": [ "16.1" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "If 4000 dollars is invested in a bank account at an interest rate of 8 per cent per year, compounded continuously. How many years will it take for your balance to reach 20000 dollars? [ANS]\nNOTE: Give your answer to the nearest tenth of a year.", "answer_v3": [ "20.1" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0232", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Continuous interest", "level": "3", "keywords": [ "algebra" ], "problem_v1": "You are investing money at 9.7 percent annual interest, compounded continuously. It will take you [ANS] years to double your investment.", "answer_v1": [ "7.14584722226748" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "You are investing money at 5.5 percent annual interest, compounded continuously. It will take you [ANS] years to double your investment.", "answer_v2": [ "12.6026760101808" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "You are investing money at 6.9 percent annual interest, compounded continuously. It will take you [ANS] years to double your investment.", "answer_v3": [ "10.045611312463" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0233", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Continuous interest", "level": "3", "keywords": [ "exponential functions", "growth rate", "growth factor" ], "problem_v1": "The dollar value of two investments after $t$ years is given by $f(t)=1100(1.17)^t$ and $g(t)=750(1.56)^t$. After how many years are the two investments worth the exact same amount?\n$t=$ [ANS]", "answer_v1": [ "[log(1100/750)]/[log(1.56/1.17)]" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "The dollar value of two investments after $t$ years is given by $f(t)=900(1.1)^t$ and $g(t)=600(1.77)^t$. After how many years are the two investments worth the exact same amount?\n$t=$ [ANS]", "answer_v2": [ "[log(900/600)]/[log(1.77/1.1)]" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "The dollar value of two investments after $t$ years is given by $f(t)=1000(1.13)^t$ and $g(t)=700(1.57)^t$. After how many years are the two investments worth the exact same amount?\n$t=$ [ANS]", "answer_v3": [ "[log(1000/700)]/[log(1.57/1.13)]" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0234", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Continuous interest", "level": "3", "keywords": [ "finance", "bond" ], "problem_v1": "Sam Spender's current annual salary is \\$55000. How much will he need to earn 11 years from now in order to retain his present lifestyle if the rate of inflation over this period is 3.75\\% per year compounded continuously. (Round your answer to 2 decimal places.) \\$ [ANS]", "answer_v1": [ "83082.42" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Sam Spender's current annual salary is \\$41000. How much will he need to earn 8 years from now in order to retain his present lifestyle if the rate of inflation over this period is 5\\% per year compounded continuously. (Round your answer to 2 decimal places.) \\$ [ANS]", "answer_v2": [ "61164.81" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Sam Spender's current annual salary is \\$46000. How much will he need to earn 9 years from now in order to retain his present lifestyle if the rate of inflation over this period is 3.75\\% per year compounded continuously. (Round your answer to 2 decimal places.) \\$ [ANS]", "answer_v3": [ "64466.22" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0235", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Continuous interest", "level": "3", "keywords": [ "financial mathematics", "compound interest" ], "problem_v1": "Jaco wants to buy a new bass guitar which costs $\\\\$3{,}499.99$ plus tax. If his state's sale tax is $8.045 \\%$ and he saves for $30$ months, how much should he deposit into a bank account earning an annual interest rate of $4.483 \\%$ compounded continuously if he wants to meet his goal? Jaco needs to deposit $[ANS].", "answer_v1": [ "3380.63" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Jaco wants to buy a new bass guitar which costs $\\\\$1{,}799.99$ plus tax. If his state's sale tax is $8.655 \\%$ and he saves for $20$ months, how much should he deposit into a bank account earning an annual interest rate of $2.598 \\%$ compounded continuously if he wants to meet his goal? Jaco needs to deposit $[ANS].", "answer_v2": [ "1872.90" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Jaco wants to buy a new bass guitar which costs $\\\\$2{,}399.99$ plus tax. If his state's sale tax is $8.085 \\%$ and he saves for $25$ months, how much should he deposit into a bank account earning an annual interest rate of $3.114 \\%$ compounded continuously if he wants to meet his goal? Jaco needs to deposit $[ANS].", "answer_v3": [ "2431.08" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0236", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Force of interest", "level": "3", "keywords": [], "problem_v1": "Find $n$ such that $1+\\frac{i^{(n)}}{n}=(1+\\frac{i^{(5)}}{5})/(1+\\frac{i^{(7)}}{7})$ where $i^{(5)}$, $i^{(7)}$, $i^{(n)}$ all produce the same effective rate of interest. $n$=[ANS]", "answer_v1": [ "17.5" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Find $n$ such that $1+\\frac{i^{(n)}}{n}=(1+\\frac{i^{(2)}}{2})/(1+\\frac{i^{(5)}}{5})$ where $i^{(2)}$, $i^{(5)}$, $i^{(n)}$ all produce the same effective rate of interest. $n$=[ANS]", "answer_v2": [ "3.33333333333333" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Find $n$ such that $1+\\frac{i^{(n)}}{n}=(1+\\frac{i^{(3)}}{3})/(1+\\frac{i^{(5)}}{5})$ where $i^{(3)}$, $i^{(5)}$, $i^{(n)}$ all produce the same effective rate of interest. $n$=[ANS]", "answer_v3": [ "7.5" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0237", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Force of interest", "level": "4", "keywords": [ "force of interest" ], "problem_v1": "On January 1, 2004, Sam invests \\$ 1000 in a fund for which the force of interest at time t is expressed by $\\delta_t=(0.1)(t-1)^{8}$, where t is the number of years since January 1, 2004. Calculate the accumulated value of the fund on January 1, 2013. $\\delta_t=$ [ANS]", "answer_v1": [ "1491308100" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "On January 1, 2004, Sam invests \\$ 1000 in a fund for which the force of interest at time t is expressed by $\\delta_t=(0.1)(t-1)^{2}$, where t is the number of years since January 1, 2004. Calculate the accumulated value of the fund on January 1, 2016. $\\delta_t=$ [ANS]", "answer_v2": [ "44400" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "On January 1, 2004, Sam invests \\$ 1000 in a fund for which the force of interest at time t is expressed by $\\delta_t=(0.1)(t-1)^{4}$, where t is the number of years since January 1, 2004. Calculate the accumulated value of the fund on January 1, 2013. $\\delta_t=$ [ANS]", "answer_v3": [ "655380" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0238", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Force of interest", "level": "4", "keywords": [ "compound interest", "force of interest" ], "problem_v1": "Fund A accumulates at a rate of 12 \\% convertible monthly. Fund B accumulates with force of interest of $\\delta_t=\\frac{t}{15}$ for all t. At time t=0, \\$ 1 is deposited in each fund. The positive time, in years, that the two funds are equal is denoted by T. Calculate T. T=[ANS] years.", "answer_v1": [ "3.58211910714051" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Fund A accumulates at a rate of 3 \\% convertible monthly. Fund B accumulates with force of interest of $\\delta_t=\\frac{t}{24}$ for all t. At time t=0, \\$ 1 is deposited in each fund. The positive time, in years, that the two funds are equal is denoted by T. Calculate T. T=[ANS] years.", "answer_v2": [ "1.4382029943862" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Fund A accumulates at a rate of 6 \\% convertible monthly. Fund B accumulates with force of interest of $\\delta_t=\\frac{t}{16}$ for all t. At time t=0, \\$ 1 is deposited in each fund. The positive time, in years, that the two funds are equal is denoted by T. Calculate T. T=[ANS] years.", "answer_v3": [ "1.91521594023896" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0239", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Force of interest", "level": "4", "keywords": [ "force of interest", "discount rate" ], "problem_v1": "You are given $\\delta_t=\\frac{3}{t+1}$ for $2 \\le t \\le 9$. For the one year interval between 3 and 4, calculate the equivalent $d^{(5)}$. $d^{(5)}$=[ANS] \\%", "answer_v1": [ "79.2668204576752" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "You are given $\\delta_t=\\frac{4}{t+1}$ for $2 \\le t \\le 5$. For the one year interval between 3 and 4, calculate the equivalent $d^{(2)}$. $d^{(2)}$=[ANS] \\%", "answer_v2": [ "87.5" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "You are given $\\delta_t=\\frac{3}{t+1}$ for $2 \\le t \\le 6$. For the one year interval between 3 and 4, calculate the equivalent $d^{(3)}$. $d^{(3)}$=[ANS] \\%", "answer_v3": [ "75" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0240", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Force of interest", "level": "4", "keywords": [ "continuous payments" ], "problem_v1": "You are given $\\delta_t=\\frac{5}{t+10}$ for all non-negative t. Calculate $\\overline {a}_{4\\rceil}$. $\\overline {a}_{4\\rceil}$=[ANS].", "answer_v1": [ "1.84922948771345" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "You are given $\\delta_t=\\frac{2}{t+10}$ for all non-negative t. Calculate $\\overline {a}_{5\\rceil}$. $\\overline {a}_{5\\rceil}$=[ANS].", "answer_v2": [ "3.33333333333333" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "You are given $\\delta_t=\\frac{3}{t+10}$ for all non-negative t. Calculate $\\overline {a}_{4\\rceil}$. $\\overline {a}_{4\\rceil}$=[ANS].", "answer_v3": [ "2.44897959183673" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0241", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Force of interest", "level": "4", "keywords": [ "compound interest", "force of interest", "future value" ], "problem_v1": "Two funds, X and Y start with the same amount. Given the information below, calculate i. i) Fund X accumulates at a force of interest of 12 \\%. ii) Fund Y accumulates at a rate of interest i, compounded quarterly. iii) At the end of 9 years, fund X is 1.12 times as large as Fund Y.\nInterest rate i=[ANS] \\%?", "answer_v1": [ "10.8862974811327" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Two funds, X and Y start with the same amount. Given the information below, calculate i. i) Fund X accumulates at a force of interest of 3 \\%. ii) Fund Y accumulates at a rate of interest i, compounded semiannually. iii) At the end of 6 years, fund X is 1.03 times as large as Fund Y.\nInterest rate i=[ANS] \\%?", "answer_v2": [ "2.52313620225286" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Two funds, X and Y start with the same amount. Given the information below, calculate i. i) Fund X accumulates at a force of interest of 6 \\%. ii) Fund Y accumulates at a rate of interest i, compounded quarterly. iii) At the end of 7 years, fund X is 1.06 times as large as Fund Y.\nInterest rate i=[ANS] \\%?", "answer_v3": [ "5.20111111803399" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0242", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "3", "keywords": [ "financial mathematics", "present and future value" ], "problem_v1": "Suppose that a payment in three years of 13000 dollars has a present value of 9866.48 dollars. What is the nominal rate of interest convertible quarterly? Answer=[ANS] percent.", "answer_v1": [ "9.3" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose that a payment in three years of 7000 dollars has a present value of 5099.42 dollars. What is the nominal rate of interest convertible quarterly? Answer=[ANS] percent.", "answer_v2": [ "10.7" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose that a payment in three years of 9000 dollars has a present value of 6810.64 dollars. What is the nominal rate of interest convertible quarterly? Answer=[ANS] percent.", "answer_v3": [ "9.4" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0243", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "3", "keywords": [ "financial mathematics", "effective and nominal rates" ], "problem_v1": "Suppose that a savings account pays an effective rate of interest of 10.8 percent. What is the equivalent quarterly compound interest rate? Answer=[ANS] percent.", "answer_v1": [ "2.5970657160945" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose that a savings account pays an effective rate of interest of 7.4 percent. What is the equivalent quarterly compound interest rate? Answer=[ANS] percent.", "answer_v2": [ "1.80077173786697" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose that a savings account pays an effective rate of interest of 8.5 percent. What is the equivalent quarterly compound interest rate? Answer=[ANS] percent.", "answer_v3": [ "2.0604395836106" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0244", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "3", "keywords": [ "financial mathematics", "effective and nominal rates" ], "problem_v1": "Suppose that 7600 dollars is borrowed at a nominal interest rate of 7.8 percent convertible monthly. How much is owed in 8 years?\nAnswer=[ANS] dollars.", "answer_v1": [ "14155.8645304057" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose that 6000 dollars is borrowed at a nominal interest rate of 9 percent convertible monthly. How much is owed in 5 years?\nAnswer=[ANS] dollars.", "answer_v2": [ "9394.08616164942" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose that 6600 dollars is borrowed at a nominal interest rate of 7.8 percent convertible monthly. How much is owed in 6 years?\nAnswer=[ANS] dollars.", "answer_v3": [ "10522.9144516068" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0245", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "3", "keywords": [ "financial mathematics", "effective and nominal rates" ], "problem_v1": "Suppose that a money market fund pays a nominal rate of interest of 10.8 percent convertible semiannually. What is the equivalent nominal rate convertible monthly? Answer=[ANS] percent.", "answer_v1": [ "10.5647244431156" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose that a money market fund pays a nominal rate of interest of 7.4 percent convertible semiannually. What is the equivalent nominal rate convertible monthly? Answer=[ANS] percent.", "answer_v2": [ "7.2884304741601" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose that a money market fund pays a nominal rate of interest of 8.5 percent convertible semiannually. What is the equivalent nominal rate convertible monthly? Answer=[ANS] percent.", "answer_v3": [ "8.35327454702934" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0246", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "3", "keywords": [ "financial mathematics", "effective and nominal rates" ], "problem_v1": "An investment will quadruple your money in 10 years. What is the nominal rate of interest convertible quarterly? Answer=[ANS] percent.", "answer_v1": [ "14.105969536551" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "An investment will double your money in 12 years. What is the nominal rate of interest convertible quarterly? Answer=[ANS] percent.", "answer_v2": [ "5.8181339750095" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "An investment will double your money in 11 years. What is the nominal rate of interest convertible quarterly? Answer=[ANS] percent.", "answer_v3": [ "6.35123324222056" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0247", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "3", "keywords": [ "financial mathematics", "effective and nominal rates" ], "problem_v1": "Wilma invests 19000 dollars at 10.5 percent nominal interest convertible quarterly. After 4 years, she withdraws 7000 dollars. How much is the investment worth after 7 years?\nAnswer=[ANS] dollars.", "answer_v1": [ "29697.3256317481" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Wilma invests 16000 dollars at 7.8 percent nominal interest convertible quarterly. After 4 years, she withdraws 8000 dollars. How much is the investment worth after 7 years?\nAnswer=[ANS] dollars.", "answer_v2": [ "17390.1511854789" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Wilma invests 17000 dollars at 8.5 percent nominal interest convertible quarterly. After 4 years, she withdraws 7000 dollars. How much is the investment worth after 7 years?\nAnswer=[ANS] dollars.", "answer_v3": [ "21620.8605211206" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0248", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "5", "keywords": [ "exponential functions", "compound interest", "effective rate", "nominal rate", "continuous exponential growth" ], "problem_v1": "What is the balance after 1 year of an account containing \\$1300 which earns a yearly nominal interest of 10\\% that is compounded (round all answers to the nearest cent; do not write your answers with commas) (round all answers to the nearest cent; do not write your answers with commas):\n(a) annually? \\$ [ANS]\n(b) weekly (there are 52 weeks per year)? \\$ [ANS]\n(c) every minute (there are 525,600 minutes per year)? \\$ [ANS]\n(d) continuously? \\$ [ANS]", "answer_v1": [ "1430", "1436.58", "1436.72", "1436.72" ], "answer_type_v1": [ "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [] ], "problem_v2": "What is the balance after 1 year of an account containing \\$600 which earns a yearly nominal interest of 12\\% that is compounded (round all answers to the nearest cent; do not write your answers with commas) (round all answers to the nearest cent; do not write your answers with commas):\n(a) annually? \\$ [ANS]\n(b) weekly (there are 52 weeks per year)? \\$ [ANS]\n(c) every minute (there are 525,600 minutes per year)? \\$ [ANS]\n(d) continuously? \\$ [ANS]", "answer_v2": [ "672", "676.4", "676.5", "676.5" ], "answer_type_v2": [ "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [] ], "problem_v3": "What is the balance after 1 year of an account containing \\$900 which earns a yearly nominal interest of 11\\% that is compounded (round all answers to the nearest cent; do not write your answers with commas) (round all answers to the nearest cent; do not write your answers with commas):\n(a) annually? \\$ [ANS]\n(b) weekly (there are 52 weeks per year)? \\$ [ANS]\n(c) every minute (there are 525,600 minutes per year)? \\$ [ANS]\n(d) continuously? \\$ [ANS]", "answer_v3": [ "999", "1004.53", "1004.65", "1004.65" ], "answer_type_v3": [ "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [] ] }, { "id": "Financial_mathematics_0249", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "5", "keywords": [ "exponential functions", "compound interest", "effective rate", "nominal rate", "continuous exponential growth" ], "problem_v1": "A sum of \\$850 is invested for 10 years and the interest is compounded quarterly. There is \\$1050 in the account at the end of 10 years. What is the nominal annual rate? [ANS] \\%", "answer_v1": [ "2.11868223885926" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A sum of \\$700 is invested for 10 years and the interest is compounded quarterly. There is \\$950 in the account at the end of 10 years. What is the nominal annual rate? [ANS] \\%", "answer_v2": [ "3.06550348332239" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A sum of \\$750 is invested for 10 years and the interest is compounded quarterly. There is \\$950 in the account at the end of 10 years. What is the nominal annual rate? [ANS] \\%", "answer_v3": [ "2.37088651697696" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0250", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "5", "keywords": [ "exponential functions", "compound interest", "effective rate", "nominal rate", "continuous exponential growth" ], "problem_v1": "Three different investments are given in the table below.\n(a) Find the balance of each investment after the two year period. Fill in correct answers in the blanks beside each investment (round all dollar figures to the nearest cent.) (round all dollar figures to the nearest cent.):\n$\\begin{array}{cccc}\\hline Investment A & \\$975 deposited at 6.3\\% per year compounded continuously for two years. & \\$ & [ANS] \\\\\\hlineInvestment B & \\$1075 deposited at 4\\% per year compounded monthly for two years. & \\$ & [ANS] \\\\\\hlineInvestment C & \\$875 deposited at 14.5\\% per year compounded daily (365 days per year) for two years. & \\$ & [ANS] \\\\\\hline\\end{array}$\n(b) Rank these three investments from best to worst in terms of rate of return: The best rate of return is Investment [ANS] The second best rate of return is Investment [ANS] The worst rate of return is Investment [ANS]", "answer_v1": [ "1105.93", "1164.38", "1169.31", "C", "A", "B" ], "answer_type_v1": [ "NV", "NV", "NV", "MCS", "MCS", "MCS" ], "options_v1": [ [], [], [], [ "A", "B", "C" ], [ "A", "B", "C" ], [ "A", "B", "C" ] ], "problem_v2": "Three different investments are given in the table below.\n(a) Find the balance of each investment after the two year period. Fill in correct answers in the blanks beside each investment (round all dollar figures to the nearest cent.) (round all dollar figures to the nearest cent.):\n$\\begin{array}{cccc}\\hline Investment A & \\$800 deposited at 13.5\\% per year compounded daily (365 days per year) for two years. & \\$ & [ANS] \\\\\\hlineInvestment B & \\$1000 deposited at 6.9\\% per year compounded continuously for two years. & \\$ & [ANS] \\\\\\hlineInvestment C & \\$1025 deposited at 4\\% per year compounded monthly for two years. & \\$ & [ANS] \\\\\\hline\\end{array}$\n(b) Rank these three investments from best to worst in terms of rate of return: The best rate of return is Investment [ANS] The second best rate of return is Investment [ANS] The worst rate of return is Investment [ANS]", "answer_v2": [ "1047.92", "1147.98", "1110.22", "A", "B", "C" ], "answer_type_v2": [ "NV", "NV", "NV", "MCS", "MCS", "MCS" ], "options_v2": [ [], [], [], [ "A", "B", "C" ], [ "A", "B", "C" ], [ "A", "B", "C" ] ], "problem_v3": "Three different investments are given in the table below.\n(a) Find the balance of each investment after the two year period. Fill in correct answers in the blanks beside each investment (round all dollar figures to the nearest cent.) (round all dollar figures to the nearest cent.):\n$\\begin{array}{cccc}\\hline Investment A & \\$1050 deposited at 4\\% per year compounded monthly for two years. & \\$ & [ANS] \\\\\\hlineInvestment B & \\$975 deposited at 6.3\\% per year compounded continuously for two years. & \\$ & [ANS] \\\\\\hlineInvestment C & \\$825 deposited at 13.5\\% per year compounded daily (365 days per year) for two years. & \\$ & [ANS] \\\\\\hline\\end{array}$\n(b) Rank these three investments from best to worst in terms of rate of return: The best rate of return is Investment [ANS] The second best rate of return is Investment [ANS] The worst rate of return is Investment [ANS]", "answer_v3": [ "1137.3", "1105.93", "1080.67", "C", "B", "A" ], "answer_type_v3": [ "NV", "NV", "NV", "MCS", "MCS", "MCS" ], "options_v3": [ [], [], [], [ "A", "B", "C" ], [ "A", "B", "C" ], [ "A", "B", "C" ] ] }, { "id": "Financial_mathematics_0251", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "3", "keywords": [ "algebra" ], "problem_v1": "Over $7$ years, the original principal of \\$1377 accumulated to \\$2291 in an account in which interest was compounded monthly. Determine the APR. APR=[ANS] $\\%$", "answer_v1": [ "7.29467065174623" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Over $3$ years, the original principal of \\$1041 accumulated to \\$2466 in an account in which interest was compounded monthly. Determine the APR. APR=[ANS] $\\%$", "answer_v2": [ "29.094286989011" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Over $4$ years, the original principal of \\$1157 accumulated to \\$2303 in an account in which interest was compounded monthly. Determine the APR. APR=[ANS] $\\%$", "answer_v3": [ "17.3335500094403" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0252", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "2", "keywords": [ "algebra" ], "problem_v1": "What effective rate is equivalent to a nominal rate of $18\\%$ compounded monthly? $r_{e}=$ [ANS] $\\%$", "answer_v1": [ "19.5618171461534" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "What effective rate is equivalent to a nominal rate of $10\\%$ compounded monthly? $r_{e}=$ [ANS] $\\%$", "answer_v2": [ "10.4713067441297" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "What effective rate is equivalent to a nominal rate of $13\\%$ compounded monthly? $r_{e}=$ [ANS] $\\%$", "answer_v3": [ "13.8032481613877" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0253", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "3", "keywords": [ "algebra" ], "problem_v1": "A credit card company has finance charge of \\$2.3 per month on the outstanding indebtedness. What is the effective rate? $r_{e}=$ [ANS] $\\%$", "answer_v1": [ "31.3734498399601" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A credit card company has finance charge of \\$1.6 per month on the outstanding indebtedness. What is the effective rate? $r_{e}=$ [ANS] $\\%$", "answer_v2": [ "20.9830406509082" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A credit card company has finance charge of \\$1.9 per month on the outstanding indebtedness. What is the effective rate? $r_{e}=$ [ANS] $\\%$", "answer_v3": [ "25.3401494152225" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0254", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "2", "keywords": [ "algebra" ], "problem_v1": "Billy Ray put \\$ $1377$ in his savings account $7$ years ago. The money was compounded quarterly, and has amounted to \\$ $2291$. Determine the nominal rate. APR=[ANS] $\\%$", "answer_v1": [ "7.33910402149665" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Billy Ray put \\$ $1041$ in his savings account $3$ years ago. The money was compounded quarterly, and has amounted to \\$ $2466$. Determine the nominal rate. APR=[ANS] $\\%$", "answer_v2": [ "29.8053857824789" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Billy Ray put \\$ $1157$ in his savings account $4$ years ago. The money was compounded quarterly, and has amounted to \\$ $2303$. Determine the nominal rate. APR=[ANS] $\\%$", "answer_v3": [ "17.5851321715585" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0255", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "3", "keywords": [ "algebra" ], "problem_v1": "Dan has a choice of investing a sum of money at $9\\%$ compounded monthly or at $8.5\\%$ compounded daily. Calculate the effective rate in each case to determine the better rate. $9\\%$ compounded monthly is equivalent to $r_{e}$ of [ANS] $\\%$ $8.5\\%$ compounded daily is equivalent to $r_{e}$ of [ANS] $\\%$", "answer_v1": [ "9.38068976709838", "8.87062931081102" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Dan has a choice of investing a sum of money at $4\\%$ compounded monthly or at $3.5\\%$ compounded daily. Calculate the effective rate in each case to determine the better rate. $4\\%$ compounded monthly is equivalent to $r_{e}$ of [ANS] $\\%$ $3.5\\%$ compounded daily is equivalent to $r_{e}$ of [ANS] $\\%$", "answer_v2": [ "4.07415429197906", "3.56179710571844" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Dan has a choice of investing a sum of money at $6\\%$ compounded monthly or at $5.5\\%$ compounded daily. Calculate the effective rate in each case to determine the better rate. $6\\%$ compounded monthly is equivalent to $r_{e}$ of [ANS] $\\%$ $5.5\\%$ compounded daily is equivalent to $r_{e}$ of [ANS] $\\%$", "answer_v3": [ "6.16778118644983", "5.65362369937314" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0256", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "3", "keywords": [ "algebra" ], "problem_v1": "Suppose attending a certain college cost \\$30000 in the 2000-2001 school year. Assuming an effective $5\\%$ inflation rate, determine what the college costs will be in the 2008-2009 school year. \\$ [ANS]", "answer_v1": [ "44323.6633136719" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose attending a certain college cost \\$16000 in the 2000-2001 school year. Assuming an effective $8\\%$ inflation rate, determine what the college costs will be in the 2008-2009 school year. \\$ [ANS]", "answer_v2": [ "29614.8833645101" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose attending a certain college cost \\$21000 in the 2000-2001 school year. Assuming an effective $5\\%$ inflation rate, determine what the college costs will be in the 2008-2009 school year. \\$ [ANS]", "answer_v3": [ "31026.5643195703" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0257", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "3", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "Find the effective rate of interest for a) 12\\% compounded monthly Answer=[ANS] \\% b) 9\\% compounded semiannually Answer=[ANS] \\%", "answer_v1": [ "12.682503013197", "9.20249999999998" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Find the effective rate of interest for a) 4\\% compounded monthly Answer=[ANS] \\% b) 12\\% compounded semiannually Answer=[ANS] \\%", "answer_v2": [ "4.07415429197906", "12.36" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Find the effective rate of interest for a) 7\\% compounded monthly Answer=[ANS] \\% b) 9\\% compounded semiannually Answer=[ANS] \\%", "answer_v3": [ "7.22900808562359", "9.20249999999998" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0258", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "3", "keywords": [ "finance", "effective annual rate" ], "problem_v1": "Joy Holmes purchased a house in January, 2003 for \\$312000. In January, 2008 she sold the house and made a net profit of \\$75000. Find the effective annual rate of return on her investment over the 5 year period. [ANS]", "answer_v1": [ "0.04402590361465" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Joy Holmes purchased a house in January, 2000 for \\$265000. In January, 2006 she sold the house and made a net profit of \\$67000. Find the effective annual rate of return on her investment over the 6 year period. [ANS]", "answer_v2": [ "0.03828208788824" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Joy Holmes purchased a house in January, 2001 for \\$278000. In January, 2006 she sold the house and made a net profit of \\$71000. Find the effective annual rate of return on her investment over the 5 year period. [ANS]", "answer_v3": [ "0.046540708384317" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0259", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "4", "keywords": [ "exponential model", "growth" ], "problem_v1": "Tyler invested in company stock in the year 1999. The annual yield for his investment was 6.3\\%; however, the inflation rate was 7.3\\%.\n(a) What was the real growth rate of this investment? Answer: [ANS] \\% (b) Suppose Tyler wants to make a better investment that will have a real growth rate of 7.9\\%. What annual interest rate will he need to earn on his investment to accomplish his goal? Answer: [ANS] \\%", "answer_v1": [ "-0.931966449207829", "15.7767" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Steve invested in company stock in the year 1982. The annual yield for his investment was 5.6\\%; however, the inflation rate was 6.3\\%.\n(a) What was the real growth rate of this investment? Answer: [ANS] \\% (b) Suppose Steve wants to make a better investment that will have a real growth rate of 9.8\\%. What annual interest rate will he need to earn on his investment to accomplish his goal? Answer: [ANS] \\%", "answer_v2": [ "-0.6585136406397", "16.7174" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Tyler invested in company stock in the year 1988. The annual yield for his investment was 6.4\\%; however, the inflation rate was 8.3\\%.\n(a) What was the real growth rate of this investment? Answer: [ANS] \\% (b) Suppose Tyler wants to make a better investment that will have a real growth rate of 9.6\\%. What annual interest rate will he need to earn on his investment to accomplish his goal? Answer: [ANS] \\%", "answer_v3": [ "-1.75438596491228", "18.6968" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0260", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "3", "keywords": [ "exponential model", "growth" ], "problem_v1": "Lisa made an investment with a 10.5\\% annual yield. However, the real growth rate of her investment was only 6.7\\%. What was the inflation rate? Answer: [ANS] \\%", "answer_v1": [ "3.56138706654171" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Lenny made an investment with a 12.4\\% annual yield. However, the real growth rate of his investment was only 5.3\\%. What was the inflation rate? Answer: [ANS] \\%", "answer_v2": [ "6.74264007597341" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Barney made an investment with a 9.5\\% annual yield. However, the real growth rate of his investment was only 6.5\\%. What was the inflation rate? Answer: [ANS] \\%", "answer_v3": [ "2.8169014084507" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0261", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "3", "keywords": [], "problem_v1": "You invested 20000 on January 1, 2001. The investment was worth 27500 on July 1, 2006. The effective rate of return for the first year was 10 \\%. Determine the annualized effective rate of return from January 1, 2002, to July 1, 2006. Annualized effective rate of return=[ANS] \\%", "answer_v1": [ "5.083749007965" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "You invested 5000 on January 1, 2001. The investment was worth 28600 on July 1, 2006. The effective rate of return for the first year was 4 \\%. Determine the annualized effective rate of return from January 1, 2002, to July 1, 2006. Annualized effective rate of return=[ANS] \\%", "answer_v2": [ "46.057896631733" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "You invested 10000 on January 1, 2001. The investment was worth 23700 on July 1, 2006. The effective rate of return for the first year was 5 \\%. Determine the annualized effective rate of return from January 1, 2002, to July 1, 2006. Annualized effective rate of return=[ANS] \\%", "answer_v3": [ "19.8308602573083" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0262", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "3", "keywords": [], "problem_v1": "Which simple interest rate over six years is closest to being equivalent to the following: an effective rate of discount of 12\\% for the first year, an effective rate of discount of 10 \\% for the second year, and effective rate of discount of 10\\% for the third year, and effective rate of interest of 12\\% for the fourth, fifth, and sixth years?\nSimple annual interest rate over six years=[ANS] \\%", "answer_v1": [ "16.1833146277591" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Which simple interest rate over six years is closest to being equivalent to the following: an effective rate of discount of 3\\% for the first year, an effective rate of discount of 15 \\% for the second year, and effective rate of discount of 4\\% for the third year, and effective rate of interest of 6\\% for the fourth, fifth, and sixth years?\nSimple annual interest rate over six years=[ANS] \\%", "answer_v2": [ "8.41200053904724" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Which simple interest rate over six years is closest to being equivalent to the following: an effective rate of discount of 6\\% for the first year, an effective rate of discount of 10 \\% for the second year, and effective rate of discount of 5\\% for the third year, and effective rate of interest of 9\\% for the fourth, fifth, and sixth years?\nSimple annual interest rate over six years=[ANS] \\%", "answer_v3": [ "10.188897183858" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0263", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "3", "keywords": [], "problem_v1": "At what nominal rate of interest convertible 6 times a year will exactly triple your investment in 14 years. Annual nominal interest rate=[ANS] \\%", "answer_v1": [ "7.89877093911913" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "At what nominal rate of interest convertible 2 times a year will exactly quadruple your investment in 8 years. Annual nominal interest rate=[ANS] \\%", "answer_v2": [ "18.1015465330515" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "At what nominal rate of interest convertible 3 times a year will exactly triple your investment in 10 years. Annual nominal interest rate=[ANS] \\%", "answer_v3": [ "11.1897591908852" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0264", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "2", "keywords": [ "financial mathematics", "compound interest", "effective rate" ], "problem_v1": "Find the annual nominal rate compounded continuously which has the same APY as an investment earning $9.774 \\%$ compounded quarterly. [ANS] $\\%$ (Note: Your answer should be accurate to two decimal places)", "answer_v1": [ "9.6565" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Find the annual nominal rate compounded continuously which has the same APY as an investment earning $3.747 \\%$ compounded monthly. [ANS] $\\%$ (Note: Your answer should be accurate to two decimal places)", "answer_v2": [ "3.74116" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Find the annual nominal rate compounded continuously which has the same APY as an investment earning $5.821 \\%$ compounded quarterly. [ANS] $\\%$ (Note: Your answer should be accurate to two decimal places)", "answer_v3": [ "5.77905" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0265", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Effective and nominal rates of interest", "level": "3", "keywords": [ "financial mathematics", "compound interest" ], "problem_v1": "Suppose you deposit $\\\\$6{,}326.46$ into two different bank accounts. Account A earns an annual simple interest rate of $7.725 \\%$. Account B earns an annual interest rate of $7.725 \\%$ compounded weekly. After $9$ years, how much is in each account. How much more money interest did you earn in Account B than you did in Account A? Amount in Account A: $[ANS]\nAmount in Account B: $[ANS]\nHow much more interest did you earn in Account B than you did in Account A? $[ANS]\n", "answer_v1": [ "10724.93", "12673.01", "1948.08" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Suppose you deposit $\\\\$7{,}726.72$ into two different bank accounts. Account A earns an annual simple interest rate of $4.897 \\%$. Account B earns an annual interest rate of $4.897 \\%$ compounded quarterly. After $6$ years, how much is in each account. How much more money interest did you earn in Account B than you did in Account A? Amount in Account A: $[ANS]\nAmount in Account B: $[ANS]\nHow much more interest did you earn in Account B than you did in Account A? $[ANS]\n", "answer_v2": [ "9996.98", "10347.25", "350.26" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Suppose you deposit $\\\\$6{,}421.71$ into two different bank accounts. Account A earns an annual simple interest rate of $5.671 \\%$. Account B earns an annual interest rate of $5.671 \\%$ compounded daily. After $7$ years, how much is in each account. How much more money interest did you earn in Account B than you did in Account A? Amount in Account A: $[ANS]\nAmount in Account B: $[ANS]\nHow much more interest did you earn in Account B than you did in Account A? $[ANS]\n", "answer_v3": [ "8970.94", "9550.79", "579.85" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Financial_mathematics_0266", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "4", "keywords": [ "financial mathematics", "annuities" ], "problem_v1": "When my sister was born, my parents put 2200 dollars into an account earning 5.4 percent effective interest. When I was born, my parents put 4000 dollars into the same account. Today is my birthday, and my sister is twice as old as I am. Today the account balance is 21118.38 dollars. When I turn 21, my sister and I will be allowed to use the money in the account. What will the account balance be then? (Hint: First figure out how old I am.) Answer=[ANS] dollars.", "answer_v1": [ "27470.3159573435" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "When my sister was born, my parents put 1100 dollars into an account earning 3.9 percent effective interest. When I was born, my parents put 4900 dollars into the same account. Today is my birthday, and my sister is twice as old as I am. Today the account balance is 11582.61 dollars. When I turn 21, my sister and I will be allowed to use the money in the account. What will the account balance be then? (Hint: First figure out how old I am.) Answer=[ANS] dollars.", "answer_v2": [ "15139.6301670198" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "When my sister was born, my parents put 1500 dollars into an account earning 4.3 percent effective interest. When I was born, my parents put 4100 dollars into the same account. Today is my birthday, and my sister is twice as old as I am. Today the account balance is 13014.1 dollars. When I turn 21, my sister and I will be allowed to use the money in the account. What will the account balance be then? (Hint: First figure out how old I am.) Answer=[ANS] dollars.", "answer_v3": [ "16754.0570551077" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0267", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "3", "keywords": [ "financial mathematics", "time value of money" ], "problem_v1": "Jack opens a savings account with a deposit of 1760 dollars. He plans to make another deposit of $X$ dollars in three years, with the goal of having exactly 8500 dollars in the account 11 years after it is opened. If the account pays an effective rate of 8.2 percent, what value of $X$ will allow him to reach his goal? Answer=[ANS] dollars.", "answer_v1": [ "2295.38199794577" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Jack opens a savings account with a deposit of 1080 dollars. He plans to make another deposit of $X$ dollars in three years, with the goal of having exactly 9400 dollars in the account 8 years after it is opened. If the account pays an effective rate of 7 percent, what value of $X$ will allow him to reach his goal? Answer=[ANS] dollars.", "answer_v2": [ "5379.02364714648" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Jack opens a savings account with a deposit of 1310 dollars. He plans to make another deposit of $X$ dollars in three years, with the goal of having exactly 8500 dollars in the account 9 years after it is opened. If the account pays an effective rate of 7.65 percent, what value of $X$ will allow him to reach his goal? Answer=[ANS] dollars.", "answer_v3": [ "3827.55568803597" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0268", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "4", "keywords": [ "financial mathematics", "unknown time and logarithms" ], "problem_v1": "Rhonda deposits $A$ dollars in an account paying 8.3 percent effective, and at the same time also deposits $B$ dollars in another account paying 10.3 percent effective. After 8 years have passed, the combined total in the two accounts is 53000 dollars. In another 3 years, the balance in the account paying 10.3 percent effective is three times that of the other account. What is the balance in the account paying 8.3 percent effective 13 years after the initial deposit? Answer=[ANS] dollars.", "answer_v1": [ "20564.3610000871" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Rhonda deposits $A$ dollars in an account paying 6.2 percent effective, and at the same time also deposits $B$ dollars in another account paying 8.2 percent effective. After 7 years have passed, the combined total in the two accounts is 53000 dollars. In another 2 years, the balance in the account paying 8.2 percent effective is three times that of the other account. What is the balance in the account paying 6.2 percent effective 12 years after the initial deposit? Answer=[ANS] dollars.", "answer_v2": [ "18404.9878764425" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Rhonda deposits $A$ dollars in an account paying 6.9 percent effective, and at the same time also deposits $B$ dollars in another account paying 8.9 percent effective. After 7 years have passed, the combined total in the two accounts is 53000 dollars. In another 3 years, the balance in the account paying 8.9 percent effective is three times that of the other account. What is the balance in the account paying 6.9 percent effective 12 years after the initial deposit? Answer=[ANS] dollars.", "answer_v3": [ "19279.254229568" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0269", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "3", "keywords": [ "financial mathematics", "present and future value" ], "problem_v1": "An investment will pay 7500 dollars at the beginning of 2000, 11200 dollars at the beginning of 2003, and another $X$ dollars at the beginning of 2008. If the present value of the investment at the beginning of 1994 is 12731.43 dollars and the rate of interest is 7.15 effective, what is $X$?\nAnswer=[ANS] dollars.", "answer_v1": [ "4628" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "An investment will pay 6100 dollars at the beginning of 1999, 11900 dollars at the beginning of 2005, and another $X$ dollars at the beginning of 2008. If the present value of the investment at the beginning of 1992 is 10522.33 dollars and the rate of interest is 6.65 effective, what is $X$?\nAnswer=[ANS] dollars.", "answer_v2": [ "4153" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "An investment will pay 6600 dollars at the beginning of 1999, 11200 dollars at the beginning of 2002, and another $X$ dollars at the beginning of 2009. If the present value of the investment at the beginning of 1995 is 12978.39 dollars and the rate of interest is 7.83 effective, what is $X$?\nAnswer=[ANS] dollars.", "answer_v3": [ "4278" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0270", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "4", "keywords": [ "financial mathematics", "present and future value" ], "problem_v1": "Assume that you make the following three investments: 1400 dollars now, 700 dollars in two years, and 850 dollars in 5 years. All three investments earn simple interest at the same rate. If the accumulated value of the sum of the three investments 10 years after the initial investment is 3850 dollars, what is the rate of interest? Answer=[ANS] percent.", "answer_v1": [ "3.77358490566038" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Assume that you make the following three investments: 1000 dollars now, 800 dollars in two years, and 650 dollars in 5 years. All three investments earn simple interest at the same rate. If the accumulated value of the sum of the three investments 10 years after the initial investment is 3350 dollars, what is the rate of interest? Answer=[ANS] percent.", "answer_v2": [ "4.58015267175572" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Assume that you make the following three investments: 1100 dollars now, 700 dollars in two years, and 750 dollars in 5 years. All three investments earn simple interest at the same rate. If the accumulated value of the sum of the three investments 10 years after the initial investment is 3450 dollars, what is the rate of interest? Answer=[ANS] percent.", "answer_v3": [ "4.42260442260442" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0271", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "4", "keywords": [ "financial mathematics", "present and future value" ], "problem_v1": "Imagine that you've just won the new University of Virginia MiniLottery, and have two options for the payment of your prize. The first is to receive three equal annual payments (the first coming immediately) of 7000 dollars apiece. The second is to immediately receive a single payment of 19700 dollars. If lottery Commissioner Sandridge claims that the two options are equivalent, what effective rate of interest is being assumed? Answer=[ANS] percent.", "answer_v1": [ "6.75067426196336" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Imagine that you've just won the new University of Virginia MiniLottery, and have two options for the payment of your prize. The first is to receive three equal annual payments (the first coming immediately) of 5000 dollars apiece. The second is to immediately receive a single payment of 14000 dollars. If lottery Commissioner Sandridge claims that the two options are equivalent, what effective rate of interest is being assumed? Answer=[ANS] percent.", "answer_v2": [ "7.32122812931306" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Imagine that you've just won the new University of Virginia MiniLottery, and have two options for the payment of your prize. The first is to receive three equal annual payments (the first coming immediately) of 5500 dollars apiece. The second is to immediately receive a single payment of 15500 dollars. If lottery Commissioner Sandridge claims that the two options are equivalent, what effective rate of interest is being assumed? Answer=[ANS] percent.", "answer_v3": [ "6.59646009778188" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0272", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "3", "keywords": [ "financial mathematics", "present and future value" ], "problem_v1": "What is the present value of 1800 dollars to be paid in 7 years, if the effective rate of interest is 8.2 percent?\nAnswer=[ANS] dollars.", "answer_v1": [ "1036.76822807868" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "What is the present value of 1000 dollars to be paid in 9 years, if the effective rate of interest is 6.5 percent?\nAnswer=[ANS] dollars.", "answer_v2": [ "567.353227829363" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "What is the present value of 1300 dollars to be paid in 8 years, if the effective rate of interest is 7 percent?\nAnswer=[ANS] dollars.", "answer_v3": [ "756.61183593455" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0273", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "4", "keywords": [ "financial mathematics", "present and future value" ], "problem_v1": "Bubba Jones has an offer to play pro football in the Arena League. Part of his contract calls for him to receive a signing bonus, payable as follows: 100,000 dollars immediately, 70000 dollars in two years, and 150000 dollars in 6 years. What is the present value of the signing bonus, assuming 8.2 percent effective interest?\nAnswer=[ANS] dollars.", "answer_v1": [ "253273.995529491" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Bubba Jones has an offer to play pro football in the Arena League. Part of his contract calls for him to receive a signing bonus, payable as follows: 100,000 dollars immediately, 50000 dollars in two years, and 170000 dollars in 6 years. What is the present value of the signing bonus, assuming 6.5 percent effective interest?\nAnswer=[ANS] dollars.", "answer_v2": [ "260589.764334342" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Bubba Jones has an offer to play pro football in the Arena League. Part of his contract calls for him to receive a signing bonus, payable as follows: 100,000 dollars immediately, 50000 dollars in two years, and 150000 dollars in 6 years. What is the present value of the signing bonus, assuming 7 percent effective interest?\nAnswer=[ANS] dollars.", "answer_v3": [ "243623.269986137" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0274", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "4", "keywords": [ "financial mathematics", "effective and nominal rates" ], "problem_v1": "AJ takes out a small business loan of 15500 dollars at a nominal rate of interest of 10.5 percent convertible quarterly. One year later, he repays 3500 dollars. Two years after that, the bank wants to sell AJ's loan to another institution. How much does AJ owe at that time?\nAnswer=[ANS] dollars.", "answer_v1": [ "16846.6992448891" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "AJ takes out a small business loan of 13000 dollars at a nominal rate of interest of 7.8 percent convertible quarterly. One year later, he repays 3500 dollars. Two years after that, the bank wants to sell AJ's loan to another institution. How much does AJ owe at that time?\nAnswer=[ANS] dollars.", "answer_v2": [ "12305.66738268" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "AJ takes out a small business loan of 14000 dollars at a nominal rate of interest of 8.5 percent convertible quarterly. One year later, he repays 3500 dollars. Two years after that, the bank wants to sell AJ's loan to another institution. How much does AJ owe at that time?\nAnswer=[ANS] dollars.", "answer_v3": [ "13877.0761621232" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0275", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "3", "keywords": [ "financial mathematics", "effective and nominal rates" ], "problem_v1": "Suppose that you borrow $X$ dollars from a bank on January 1, 2000. On January 1, 2013, you owe the bank 5950 dollars. If the bank charges an interest rate of 4.5 percent effective, what was $X$?\nAnswer=[ANS] dollars.", "answer_v1": [ "3357.41626406826" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose that you borrow $X$ dollars from a bank on January 1, 2000. On January 1, 2006, you owe the bank 6830 dollars. If the bank charges an interest rate of 2.6 percent effective, what was $X$?\nAnswer=[ANS] dollars.", "answer_v2": [ "5855.12995926557" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose that you borrow $X$ dollars from a bank on January 1, 2000. On January 1, 2009, you owe the bank 6010 dollars. If the bank charges an interest rate of 3.1 percent effective, what was $X$?\nAnswer=[ANS] dollars.", "answer_v3": [ "4566.11120686003" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0276", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "4", "keywords": [ "financial mathematics", "effective and nominal rates" ], "problem_v1": "Little Suzie wins 7500 dollars in the Extreme Pit-Fighting Championship, and immediately deposits the prize money in a savings account paying a nominal interest rate of 8.9 percent convertible monthly. Five months later, she withdraws 1600 dollars from the account. How much money is in the account 17 months after the initial deposit? (Assume no other deposits or withdrawals were made to the account.)\nAnswer=[ANS] dollars.", "answer_v1": [ "6755.51302479473" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Little Suzie wins 6100 dollars in the Extreme Pit-Fighting Championship, and immediately deposits the prize money in a savings account paying a nominal interest rate of 7.9 percent convertible monthly. Five months later, she withdraws 2000 dollars from the account. How much money is in the account 12 months after the initial deposit? (Assume no other deposits or withdrawals were made to the account.)\nAnswer=[ANS] dollars.", "answer_v2": [ "4505.73036895054" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Little Suzie wins 6600 dollars in the Extreme Pit-Fighting Championship, and immediately deposits the prize money in a savings account paying a nominal interest rate of 8.4 percent convertible monthly. Five months later, she withdraws 1600 dollars from the account. How much money is in the account 13 months after the initial deposit? (Assume no other deposits or withdrawals were made to the account.)\nAnswer=[ANS] dollars.", "answer_v3": [ "5534.65791799965" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0277", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "5", "keywords": [ "financial mathematics", "effective and nominal rates" ], "problem_v1": "As a finalist on Survivor X: Math 114 Survivor X: Math 114, you receive a prize of 7500 dollars, and decide to invest it in a 5-year certificate of deposit that pays 8.5 percent nominal interest convertible quarterly. How much is in the account at the end of the 5 years?\nAnswer=[ANS] dollars.", "answer_v1": [ "11420.9611494252" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "As a finalist on Survivor X: Math 114 Survivor X: Math 114, you receive a prize of 6100 dollars, and decide to invest it in a 5-year certificate of deposit that pays 9.5 percent nominal interest convertible quarterly. How much is in the account at the end of the 5 years?\nAnswer=[ANS] dollars.", "answer_v2": [ "9754.57001694932" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "As a finalist on Survivor X: Math 114 Survivor X: Math 114, you receive a prize of 6600 dollars, and decide to invest it in a 5-year certificate of deposit that pays 8.6 percent nominal interest convertible quarterly. How much is in the account at the end of the 5 years?\nAnswer=[ANS] dollars.", "answer_v3": [ "10099.7670027168" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0278", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "3", "keywords": [ "financial mathematics", "effective and nominal rates" ], "problem_v1": "Suppose that you deposit 8000 dollars in an account that earns 8.1 percent interest convertible monthly. After 18 months, you withdraw 2200 dollars from the account. What is the account balance 5 years after the original deposit?\nAnswer=[ANS] dollars.", "answer_v1": [ "9059.79919434962" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose that you deposit 5300 dollars in an account that earns 6.3 percent interest convertible monthly. After 15 months, you withdraw 2900 dollars from the account. What is the account balance 7 years after the original deposit?\nAnswer=[ANS] dollars.", "answer_v2": [ "4066.01192225707" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose that you deposit 6200 dollars in an account that earns 6.9 percent interest convertible monthly. After 16 months, you withdraw 2200 dollars from the account. What is the account balance 4 years after the original deposit?\nAnswer=[ANS] dollars.", "answer_v3": [ "5521.15902788639" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0279", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "4", "keywords": [ "financial mathematics", "effective and nominal rates" ], "problem_v1": "Two accounts are opened at the same time. You deposit 1450 dollars into the first account, which earns interest at an effective rate of 6.2 percent. At the same time, you deposit 290 dollars into the second account, which earns an effective rate of 12.5 percent. How long will it take for the balance in the first account to be exactly twice the balance in the second account? (Assume compound interest at all times.)\nAnswer=[ANS] years. (Be sure to give at least 3 decimal places of accuracy!)", "answer_v1": [ "15.8997889568699" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Two accounts are opened at the same time. You deposit 1050 dollars into the first account, which earns interest at an effective rate of 6.9 percent. At the same time, you deposit 140 dollars into the second account, which earns an effective rate of 11.7 percent. How long will it take for the balance in the first account to be exactly twice the balance in the second account? (Assume compound interest at all times.)\nAnswer=[ANS] years. (Be sure to give at least 3 decimal places of accuracy!)", "answer_v2": [ "30.0926441506661" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Two accounts are opened at the same time. You deposit 1200 dollars into the first account, which earns interest at an effective rate of 6.2 percent. At the same time, you deposit 180 dollars into the second account, which earns an effective rate of 12.1 percent. How long will it take for the balance in the first account to be exactly twice the balance in the second account? (Assume compound interest at all times.)\nAnswer=[ANS] years. (Be sure to give at least 3 decimal places of accuracy!)", "answer_v3": [ "22.2680725223036" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0280", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "3", "keywords": [ "financial mathematics", "compound interest" ], "problem_v1": "Suppose that you borrow 3100 dollars on November 19, 2003 at an effective rate of 8.1 percent. If you make no payments, how much will you owe on January 22, 2006? (Assume compound interest for whole years, and simple interest for fractional parts of a year.)\nAnswer=[ANS] dollars.", "answer_v1": [ "3673.98907998466" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose that you borrow 1900 dollars on November 7, 2003 at an effective rate of 9.4 percent. If you make no payments, how much will you owe on January 12, 2008? (Assume compound interest for whole years, and simple interest for fractional parts of a year.)\nAnswer=[ANS] dollars.", "answer_v2": [ "2767.85077436015" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose that you borrow 2300 dollars on November 10, 2003 at an effective rate of 8.2 percent. If you make no payments, how much will you owe on January 17, 2006? (Assume compound interest for whole years, and simple interest for fractional parts of a year.)\nAnswer=[ANS] dollars.", "answer_v3": [ "2733.80027165808" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0281", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "3", "keywords": [ "financial mathematics", "compound interest" ], "problem_v1": "Suppose that 3100 dollars are invested on April 1, 1997. How much is the investment worth on June 6, 1999 if the account pays 8.1 percent annual interest? (Assume interest is compounded annually for whole years, and simple interest for the fractional parts of a year.)\nAnswer=[ANS] dollars.", "answer_v1": [ "3675.59689185918" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose that 1900 dollars are invested on April 1, 1997. How much is the investment worth on June 6, 1999 if the account pays 9.4 percent annual interest? (Assume interest is compounded annually for whole years, and simple interest for the fractional parts of a year.)\nAnswer=[ANS] dollars.", "answer_v2": [ "2312.63997269479" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose that 2300 dollars are invested on April 1, 1997. How much is the investment worth on June 6, 1999 if the account pays 8.2 percent annual interest? (Assume interest is compounded annually for whole years, and simple interest for the fractional parts of a year.)\nAnswer=[ANS] dollars.", "answer_v3": [ "2732.59041660932" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0282", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "4", "keywords": [ "financial mathematics", "compound interest" ], "problem_v1": "Allan borrows 2330 dollars from his uncle. Two years later, he borrows another 1380 dollars. If his uncle charges him 8.5 percent interest compounded annually, how much does Allan owe 8 years after the first loan?\nAnswer=[ANS] dollars.", "answer_v1": [ "6726.43326997208" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Allan borrows 1850 dollars from his uncle. Two years later, he borrows another 1480 dollars. If his uncle charges him 7.7 percent interest compounded annually, how much does Allan owe 6 years after the first loan?\nAnswer=[ANS] dollars.", "answer_v2": [ "4878.37162063397" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Allan borrows 2020 dollars from his uncle. Two years later, he borrows another 1380 dollars. If his uncle charges him 8.1 percent interest compounded annually, how much does Allan owe 7 years after the first loan?\nAnswer=[ANS] dollars.", "answer_v3": [ "5521.50337097113" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0283", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "4", "keywords": [ "financial mathematics", "compound interest" ], "problem_v1": "Suzanne opens a line of credit at a local bank, and immediately borrows 1950 dollars. 4 months later, she repays 1080 dollars. 3 months after the repayment, she borrows 690 more dollars. 5 months later, she repays 710 dollars. If no other transactions take place and the interest rate is 1 percent per month (compounded monthly), how much will she owe two years after she opened the line of credit?\nAnswer=[ANS] dollars.", "answer_v1": [ "1175.30160774706" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suzanne opens a line of credit at a local bank, and immediately borrows 1550 dollars. 6 months later, she repays 1180 dollars. 3 months after the repayment, she borrows 540 more dollars. 4 months later, she repays 650 dollars. If no other transactions take place and the interest rate is 0.9 percent per month (compounded monthly), how much will she owe two years after she opened the line of credit?\nAnswer=[ANS] dollars.", "answer_v2": [ "435.692293486252" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suzanne opens a line of credit at a local bank, and immediately borrows 1690 dollars. 4 months later, she repays 1080 dollars. 3 months after the repayment, she borrows 580 more dollars. 6 months later, she repays 680 dollars. If no other transactions take place and the interest rate is 1.15 percent per month (compounded monthly), how much will she owe two years after she opened the line of credit?\nAnswer=[ANS] dollars.", "answer_v3": [ "799.458637238141" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0284", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "3", "keywords": [ "financial mathematics", "compound interest" ], "problem_v1": "Miguel deposits 5080 dollars in an account, and 5 years later the account balance is 10460 dollars. If interest is compounded monthly, what is the rate of interest per month?\nAnswer=[ANS] percent.", "answer_v1": [ "1.21101950068991" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Miguel deposits 3940 dollars in an account, and 6 years later the account balance is 7180 dollars. If interest is compounded monthly, what is the rate of interest per month?\nAnswer=[ANS] percent.", "answer_v2": [ "0.83698140520545" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Miguel deposits 4330 dollars in an account, and 5 years later the account balance is 8160 dollars. If interest is compounded monthly, what is the rate of interest per month?\nAnswer=[ANS] percent.", "answer_v3": [ "1.06172442578245" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0285", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "3", "keywords": [ "financial mathematics", "compound interest" ], "problem_v1": "Frank borrows 14000 dollars at 8.8 percent annual interest, compounded once per year, when he begins college. Four years later, how much will he owe? (Assume that he makes no payments during the four years.) Answer=[ANS] dollars.", "answer_v1": [ "19617.498005504" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Frank borrows 8000 dollars at 9.8 percent annual interest, compounded once per year, when he begins college. Four years later, how much will he owe? (Assume that he makes no payments during the four years.) Answer=[ANS] dollars.", "answer_v2": [ "11627.848038528" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Frank borrows 10000 dollars at 8.8 percent annual interest, compounded once per year, when he begins college. Four years later, how much will he owe? (Assume that he makes no payments during the four years.) Answer=[ANS] dollars.", "answer_v3": [ "14012.49857536" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0286", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "3", "keywords": [ "financial mathematics", "compound interest" ], "problem_v1": "Hannah would like to make an investment that will turn 7500 dollars into 33000 dollars in 7 years. What quarterly rate of interest, compounded four times per year, must she receive to reach her goal? Answer=[ANS] percent.", "answer_v1": [ "5.43394402971895" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Hannah would like to make an investment that will turn 5000 dollars into 37000 dollars in 4 years. What quarterly rate of interest, compounded four times per year, must she receive to reach her goal? Answer=[ANS] percent.", "answer_v2": [ "13.3253274161518" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Hannah would like to make an investment that will turn 6000 dollars into 33000 dollars in 5 years. What quarterly rate of interest, compounded four times per year, must she receive to reach her goal? Answer=[ANS] percent.", "answer_v3": [ "8.89755638341023" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0287", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "4", "keywords": [ "financial mathematics", "compound interest" ], "problem_v1": "Gordon has heard that fusion powered SUV's will be available in 10 years at a price of 145000 dollars. How much should he invest now, at 8.8 percent interest compounded annually, to have the amount required to purchase the SUV in 10 years? Answer=[ANS] dollars.", "answer_v1": [ "62384.8375634012" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Gordon has heard that fusion powered SUV's will be available in 10 years at a price of 120000 dollars. How much should he invest now, at 9.8 percent interest compounded annually, to have the amount required to purchase the SUV in 10 years? Answer=[ANS] dollars.", "answer_v2": [ "47114.8534843536" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Gordon has heard that fusion powered SUV's will be available in 10 years at a price of 130000 dollars. How much should he invest now, at 8.8 percent interest compounded annually, to have the amount required to purchase the SUV in 10 years? Answer=[ANS] dollars.", "answer_v3": [ "55931.2336775321" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0288", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "4", "keywords": [ "exponential functions", "growth rate", "growth factor" ], "problem_v1": "You owe \\$4000 on a credit card. The card charges 1.5\\% monthly interest on your balance, and requires a minimum monthly payment of 2.4\\% of your balance. All transactions (payments and interest charges) are recorded at the end of the month. You make only the minimum required payment every month and incur no additional debt.\n(a) Complete the table below for a twelve month period. The first column is your total balance on first of the month. The second column is the amount of interest charge as a result of your outstanding balance, and third column is the minimum payment which is due at the end of the month. Thus for example, on January first your initial balance is \\$4000. As a result you are charged \\$60 in interest and are required to make a minimum payment of \\$96. Thus on February first your new balance is \\$3964=\\$4000+\\$60-\\$96 \u00a0. Do not include any commas or dollar signs in your answers.\n$\\begin{array}{cccc}\\hline Month & Balance & Interest & Minimum Payment \\\\\\hlineJan & 4000 & 60 & 96 \\\\\\hlineFeb & 3964 & 59.46 & 95.14 \\\\\\hlineMar & 3928.32 & [ANS] & [ANS] \\\\\\hlineApril & [ANS] & [ANS] & [ANS] \\\\\\hlineMay & [ANS] & [ANS] & [ANS] \\\\\\hlineJune & [ANS] & [ANS] & [ANS] \\\\\\hlineJuly & [ANS] & [ANS] & [ANS] \\\\\\hlineAug & [ANS] & [ANS] & [ANS] \\\\\\hlineSept & [ANS] & [ANS] & [ANS] \\\\\\hlineOct & [ANS] & [ANS] & [ANS] \\\\\\hlineNov & [ANS] & [ANS] & [ANS] \\\\\\hlineDec & [ANS] & [ANS] & [ANS] \\\\\\hline\\end{array}$\n(b) What will be your unpaid balance on January 1 of the next year? \\$ [ANS]\n(c) Based on your answer above, how much of your debt have you paid off in the year? \\$ [ANS]\n(d) How much money did you spend on interest charges (add up all of the interest fees charged from Jan.-Dec.)? \\$ [ANS]", "answer_v1": [ "58.92", "94.28", "3892.96", "58.39", "93.43", "3857.92", "57.87", "92.59", "3823.2", "57.35", "91.76", "3788.79", "56.83", "90.93", "3754.69", "56.32", "90.11", "3720.9", "55.81", "89.3", "3687.41", "55.31", "88.5", "3654.22", "54.81", "87.7", "3621.33", "54.32", "86.91", "3588.74", "411.26", "685.39" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [] ], "problem_v2": "You owe \\$2000 on a credit card. The card charges 1.2\\% monthly interest on your balance, and requires a minimum monthly payment of 2.5\\% of your balance. All transactions (payments and interest charges) are recorded at the end of the month. You make only the minimum required payment every month and incur no additional debt.\n(a) Complete the table below for a twelve month period. The first column is your total balance on first of the month. The second column is the amount of interest charge as a result of your outstanding balance, and third column is the minimum payment which is due at the end of the month. Thus for example, on January first your initial balance is \\$2000. As a result you are charged \\$24 in interest and are required to make a minimum payment of \\$50. Thus on February first your new balance is \\$1974=\\$2000+\\$24-\\$50 \u00a0. Do not include any commas or dollar signs in your answers.\n$\\begin{array}{cccc}\\hline Month & Balance & Interest & Minimum Payment \\\\\\hlineJan & 2000 & 24 & 50 \\\\\\hlineFeb & 1974 & 23.69 & 49.35 \\\\\\hlineMar & 1948.34 & [ANS] & [ANS] \\\\\\hlineApril & [ANS] & [ANS] & [ANS] \\\\\\hlineMay & [ANS] & [ANS] & [ANS] \\\\\\hlineJune & [ANS] & [ANS] & [ANS] \\\\\\hlineJuly & [ANS] & [ANS] & [ANS] \\\\\\hlineAug & [ANS] & [ANS] & [ANS] \\\\\\hlineSept & [ANS] & [ANS] & [ANS] \\\\\\hlineOct & [ANS] & [ANS] & [ANS] \\\\\\hlineNov & [ANS] & [ANS] & [ANS] \\\\\\hlineDec & [ANS] & [ANS] & [ANS] \\\\\\hline\\end{array}$\n(b) What will be your unpaid balance on January 1 of the next year? \\$ [ANS]\n(c) Based on your answer above, how much of your debt have you paid off in the year? \\$ [ANS]\n(d) How much money did you spend on interest charges (add up all of the interest fees charged from Jan.-Dec.)? \\$ [ANS]", "answer_v2": [ "23.38", "48.71", "1923.01", "23.08", "48.08", "1898.01", "22.78", "47.45", "1873.34", "22.48", "46.83", "1848.99", "22.19", "46.22", "1824.96", "21.9", "45.62", "1801.24", "21.61", "45.03", "1777.82", "21.33", "44.45", "1754.7", "21.06", "43.87", "1731.89", "20.78", "43.3", "1709.37", "290.63", "268.28" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [] ], "problem_v3": "You owe \\$3000 on a credit card. The card charges 1.3\\% monthly interest on your balance, and requires a minimum monthly payment of 2.4\\% of your balance. All transactions (payments and interest charges) are recorded at the end of the month. You make only the minimum required payment every month and incur no additional debt.\n(a) Complete the table below for a twelve month period. The first column is your total balance on first of the month. The second column is the amount of interest charge as a result of your outstanding balance, and third column is the minimum payment which is due at the end of the month. Thus for example, on January first your initial balance is \\$3000. As a result you are charged \\$39 in interest and are required to make a minimum payment of \\$72. Thus on February first your new balance is \\$2967=\\$3000+\\$39-\\$72 \u00a0. Do not include any commas or dollar signs in your answers.\n$\\begin{array}{cccc}\\hline Month & Balance & Interest & Minimum Payment \\\\\\hlineJan & 3000 & 39 & 72 \\\\\\hlineFeb & 2967 & 38.57 & 71.21 \\\\\\hlineMar & 2934.36 & [ANS] & [ANS] \\\\\\hlineApril & [ANS] & [ANS] & [ANS] \\\\\\hlineMay & [ANS] & [ANS] & [ANS] \\\\\\hlineJune & [ANS] & [ANS] & [ANS] \\\\\\hlineJuly & [ANS] & [ANS] & [ANS] \\\\\\hlineAug & [ANS] & [ANS] & [ANS] \\\\\\hlineSept & [ANS] & [ANS] & [ANS] \\\\\\hlineOct & [ANS] & [ANS] & [ANS] \\\\\\hlineNov & [ANS] & [ANS] & [ANS] \\\\\\hlineDec & [ANS] & [ANS] & [ANS] \\\\\\hline\\end{array}$\n(b) What will be your unpaid balance on January 1 of the next year? \\$ [ANS]\n(c) Based on your answer above, how much of your debt have you paid off in the year? \\$ [ANS]\n(d) How much money did you spend on interest charges (add up all of the interest fees charged from Jan.-Dec.)? \\$ [ANS]", "answer_v3": [ "38.15", "70.42", "2902.09", "37.73", "69.65", "2870.17", "37.31", "68.88", "2838.6", "36.9", "68.13", "2807.37", "36.5", "67.38", "2776.49", "36.09", "66.64", "2745.94", "35.7", "65.9", "2715.74", "35.3", "65.18", "2685.86", "34.92", "64.46", "2656.32", "34.53", "63.75", "2627.1", "372.9", "440.7" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [] ] }, { "id": "Financial_mathematics_0289", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "3", "keywords": [ "algebra", "Compound Interest" ], "problem_v1": "You invest \\$ 8000 in Acme Inc. on January 1, 2000. Your investment returns 5 \\% compounded monthly. How much money will you have on June 30, 2007? You will have \\$ [ANS]\nAfter what month and year will you have at least \\$ 15,000? You will have at least \\$ 15,000 after [ANS] (month) [ANS] (year). Please capitalize the month and do not use any abbreviation.", "answer_v1": [ "11630.8663338578", "August", "2012" ], "answer_type_v1": [ "NV", "MCS", "NV" ], "options_v1": [ [], [ "January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December" ], [] ], "problem_v2": "You invest \\$ 1000 in Acme Inc. on January 1, 2000. Your investment returns 6.75 \\% compounded monthly. How much money will you have on June 30, 2004? You will have \\$ [ANS]\nAfter what month and year will you have at least \\$ 15,000? You will have at least \\$ 15,000 after [ANS] (month) [ANS] (year). Please capitalize the month and do not use any abbreviation.", "answer_v2": [ "1353.77758151647", "March", "2040" ], "answer_type_v2": [ "NV", "MCS", "NV" ], "options_v2": [ [], [ "January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December" ], [] ], "problem_v3": "You invest \\$ 4000 in Acme Inc. on January 1, 2000. Your investment returns 5 \\% compounded monthly. How much money will you have on June 30, 2005? You will have \\$ [ANS]\nAfter what month and year will you have at least \\$ 15,000? You will have at least \\$ 15,000 after [ANS] (month) [ANS] (year). Please capitalize the month and do not use any abbreviation.", "answer_v3": [ "5263.11486391298", "June", "2026" ], "answer_type_v3": [ "NV", "MCS", "NV" ], "options_v3": [ [], [ "January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December" ], [] ] }, { "id": "Financial_mathematics_0290", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "4", "keywords": [ "algebra" ], "problem_v1": "You deposit \\$ 110 into an account at the beginning of each month. The bank pays you 8 \\% interest per year, compounded monthly. At the end of 17 years, after 204 payments, your account contains \\$ [ANS].", "answer_v1": [ "47814.3481315085" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "You deposit \\$ 60 into an account at the beginning of each month. The bank pays you 12 \\% interest per year, compounded monthly. At the end of 6 years, after 72 payments, your account contains \\$ [ANS].", "answer_v2": [ "6345.4218313268" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "You deposit \\$ 80 into an account at the beginning of each month. The bank pays you 9 \\% interest per year, compounded monthly. At the end of 10 years, after 120 payments, your account contains \\$ [ANS].", "answer_v3": [ "15597.2507329145" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0291", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "5", "keywords": [ "algebra" ], "problem_v1": "Jessica borrowed \\$4500 from the bank in order to buy a new piano. She will pay it off by equal payments at the end of each week for 2 years. The interest rate is $7\\%$ compounded weekly. Determine the size of payments, and the total interest paid. Payments: \\$ [ANS]\nTotal interest: \\$ [ANS]", "answer_v1": [ "46.3977964359469", "325.370829338483" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Jessica borrowed \\$3100 from the bank in order to buy a new piano. She will pay it off by equal payments at the end of each week for 2 years. The interest rate is $9\\%$ compounded weekly. Determine the size of payments, and the total interest paid. Payments: \\$ [ANS]\nTotal interest: \\$ [ANS]", "answer_v2": [ "32.5965401882673", "290.040179579797" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Jessica borrowed \\$3600 from the bank in order to buy a new piano. She will pay it off by equal payments at the end of each week for 2 years. The interest rate is $7\\%$ compounded weekly. Determine the size of payments, and the total interest paid. Payments: \\$ [ANS]\nTotal interest: \\$ [ANS]", "answer_v3": [ "37.1182371487576", "260.296663470785" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0292", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "5", "keywords": [ "algebra" ], "problem_v1": "Travis decided to put \\$450 in his savings account at the end of every month. Find the amount he has at the end of $7$ years, if the money is worth $7\\%$ compounded monthly. \\$ [ANS]", "answer_v1": [ "48599.5413138137" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Travis decided to put \\$310 in his savings account at the end of every month. Find the amount he has at the end of $4$ years, if the money is worth $9\\%$ compounded monthly. \\$ [ANS]", "answer_v2": [ "17831.4204436334" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Travis decided to put \\$360 in his savings account at the end of every month. Find the amount he has at the end of $4$ years, if the money is worth $7\\%$ compounded monthly. \\$ [ANS]", "answer_v3": [ "19875.3250352106" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0293", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "5", "keywords": [ "algebra" ], "problem_v1": "The Math department purchased a copy machine for \\$ 12000. After $4$ years, the machine will be worthless. How much money should the department deposit at the end of each quarter, if the money is worth $8\\%$ compounded quarterly, in order to save enough to buy a new copy machine at the end of $4$ years? \\$ [ANS]", "answer_v1": [ "643.801510419139" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "The Math department purchased a copy machine for \\$ 12000. After $5$ years, the machine will be worthless. How much money should the department deposit at the end of each quarter, if the money is worth $3\\%$ compounded quarterly, in order to save enough to buy a new copy machine at the end of $5$ years? \\$ [ANS]", "answer_v2": [ "558.367583274435" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "The Math department purchased a copy machine for \\$ 12000. After $4$ years, the machine will be worthless. How much money should the department deposit at the end of each quarter, if the money is worth $5\\%$ compounded quarterly, in order to save enough to buy a new copy machine at the end of $4$ years? \\$ [ANS]", "answer_v3": [ "682.160664601752" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0294", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "5", "keywords": [ "algebra" ], "problem_v1": "Brooke is buying a new sailing boat. She can afford \\$1800 monthly payments. If the store charges $7\\%$ interest rate, compounded monthly, and Brooke wants to pay off her loan in $8$ years, what is the most expensive boat she can buy?\nBoat price=\\$ [ANS]", "answer_v1": [ "132025.623633784" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Brooke is buying a new sailing boat. She can afford \\$1000 monthly payments. If the store charges $9\\%$ interest rate, compounded monthly, and Brooke wants to pay off her loan in $5$ years, what is the most expensive boat she can buy?\nBoat price=\\$ [ANS]", "answer_v2": [ "48173.373520964" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Brooke is buying a new sailing boat. She can afford \\$1300 monthly payments. If the store charges $7\\%$ interest rate, compounded monthly, and Brooke wants to pay off her loan in $6$ years, what is the most expensive boat she can buy?\nBoat price=\\$ [ANS]", "answer_v3": [ "76250.7775533632" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0295", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "5", "keywords": [ "algebra" ], "problem_v1": "Bob an Liz are buying a house. They have \\$28000 for a down payment. The house price is \\$168000. If the interest rate is $7\\%$ compounded monthly, determine the size of the monthly payments they must make over the next $22$ years to pay off the house. \\$ [ANS]", "answer_v1": [ "1040.79374144056" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Bob an Liz are buying a house. They have \\$20000 for a down payment. The house price is \\$178000. If the interest rate is $4\\%$ compounded monthly, determine the size of the monthly payments they must make over the next $18$ years to pay off the house. \\$ [ANS]", "answer_v2": [ "1027.31235971173" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Bob an Liz are buying a house. They have \\$23000 for a down payment. The house price is \\$168000. If the interest rate is $5\\%$ compounded monthly, determine the size of the monthly payments they must make over the next $21$ years to pay off the house. \\$ [ANS]", "answer_v3": [ "930.492041363992" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0296", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "5", "keywords": [ "algebra" ], "problem_v1": "The Math department also purchased a printer. After $4$ years, it will have a salvage value of \\$400. A new printer is expected to cost \\$1600. The department established a sinking fund in order to provide money for the difference between the cost and the salvage value. If the fund earns $7\\%$ compounded semiannually, determine the size of payments. \\$ [ANS]", "answer_v1": [ "132.571975858289" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "The Math department also purchased a printer. After $3$ years, it will have a salvage value of \\$100. A new printer is expected to cost \\$2000. The department established a sinking fund in order to provide money for the difference between the cost and the salvage value. If the fund earns $4\\%$ compounded semiannually, determine the size of payments. \\$ [ANS]", "answer_v2": [ "301.199043436885" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "The Math department also purchased a printer. After $3$ years, it will have a salvage value of \\$200. A new printer is expected to cost \\$1600. The department established a sinking fund in order to provide money for the difference between the cost and the salvage value. If the fund earns $4\\%$ compounded semiannually, determine the size of payments. \\$ [ANS]", "answer_v3": [ "221.936137269283" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0297", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "5", "keywords": [ "algebra" ], "problem_v1": "To open a restaurant, Nenad borrowed \\$18000 from the bank. The interest rate is $7\\%$ compounded monthly. Nenad wants to pay off the loan in $8$ years. Determine the size of each payment. \\$ [ANS]\nAfter 2 years, Nenad earned enough money to pay off the entire loan. Find the amount he must pay. \\$ [ANS]", "answer_v1": [ "245.406907449056", "14394.2057768898" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "To open a restaurant, Nenad borrowed \\$10000 from the bank. The interest rate is $9\\%$ compounded monthly. Nenad wants to pay off the loan in $5$ years. Determine the size of each payment. \\$ [ANS]\nAfter 2 years, Nenad earned enough money to pay off the entire loan. Find the amount he must pay. \\$ [ANS]", "answer_v2": [ "207.583552263539", "6527.83954140096" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "To open a restaurant, Nenad borrowed \\$13000 from the bank. The interest rate is $7\\%$ compounded monthly. Nenad wants to pay off the loan in $6$ years. Determine the size of each payment. \\$ [ANS]\nAfter 2 years, Nenad earned enough money to pay off the entire loan. Find the amount he must pay. \\$ [ANS]", "answer_v3": [ "221.637084135604", "9255.60927234736" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0298", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "5", "keywords": [ "algebra" ], "problem_v1": "Tina is buying a new apartment. She can afford a mortgage payment of \\$1580 a month, and a downpayment of \\$18000. She obtained a $22$ year loan at $7\\%$ compounded monthly. What is the most expensive apartment she can buy? Apartment price=\\$ [ANS]", "answer_v1": [ "230530.101971826" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Tina is buying a new apartment. She can afford a mortgage payment of \\$1940 a month, and a downpayment of \\$10000. She obtained a $18$ year loan at $4\\%$ compounded monthly. What is the most expensive apartment she can buy? Apartment price=\\$ [ANS]", "answer_v2": [ "308370.789665193" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Tina is buying a new apartment. She can afford a mortgage payment of \\$1610 a month, and a downpayment of \\$13000. She obtained a $21$ year loan at $4\\%$ compounded monthly. What is the most expensive apartment she can buy? Apartment price=\\$ [ANS]", "answer_v3": [ "287192.338091664" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0299", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "5", "keywords": [ "algebra" ], "problem_v1": "A small airline company wishes to lease an airplane during the 5 month long tourist season. The rental fee is \\$28000 a month, payable in advance. The company wishes to pay in advance at the beginning of the rental period to cover all the rental fees due over the 5 month period. If the money is worth $6\\%$ compounded monthly, determine the size of each payment. \\$ [ANS]", "answer_v1": [ "138613.878472699" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A small airline company wishes to lease an airplane during the 5 month long tourist season. The rental fee is \\$20000 a month, payable in advance. The company wishes to pay in advance at the beginning of the rental period to cover all the rental fees due over the 5 month period. If the money is worth $8\\%$ compounded monthly, determine the size of each payment. \\$ [ANS]", "answer_v2": [ "98684.2392274669" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A small airline company wishes to lease an airplane during the 5 month long tourist season. The rental fee is \\$23000 a month, payable in advance. The company wishes to pay in advance at the beginning of the rental period to cover all the rental fees due over the 5 month period. If the money is worth $7\\%$ compounded monthly, determine the size of each payment. \\$ [ANS]", "answer_v3": [ "113673.827800759" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0300", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "5", "keywords": [ "algebra" ], "problem_v1": "Suppose a company offers you a sales position with your choice of two methods of determining your yearly salary. One method pays \\$2200 plus a bonus of 4\\% of your yearly sales. The other method pays a straight 8\\% commission on your sales. For what yearly sales amount $S$ is it better to choose the first method?\nInstructions: Enter either $<$, $>$, $>=$ or $<=$ in the first answer box. Enter a number in the second answer box. Answer: S [ANS] [ANS] units", "answer_v1": [ "<", "55000" ], "answer_type_v1": [ "MCS", "NV" ], "options_v1": [ [ "<", ">", ">=", "<=" ], [] ], "problem_v2": "Suppose a company offers you a sales position with your choice of two methods of determining your yearly salary. One method pays \\$800 plus a bonus of 5\\% of your yearly sales. The other method pays a straight 7\\% commission on your sales. For what yearly sales amount $S$ is it better to choose the first method?\nInstructions: Enter either $<$, $>$, $>=$ or $<=$ in the first answer box. Enter a number in the second answer box. Answer: S [ANS] [ANS] units", "answer_v2": [ "<", "40000" ], "answer_type_v2": [ "MCS", "NV" ], "options_v2": [ [ "<", ">", ">=", "<=" ], [] ], "problem_v3": "Suppose a company offers you a sales position with your choice of two methods of determining your yearly salary. One method pays \\$1350 plus a bonus of 4\\% of your yearly sales. The other method pays a straight 7\\% commission on your sales. For what yearly sales amount $S$ is it better to choose the first method?\nInstructions: Enter either $<$, $>$, $>=$ or $<=$ in the first answer box. Enter a number in the second answer box. Answer: S [ANS] [ANS] units", "answer_v3": [ "<", "45000" ], "answer_type_v3": [ "MCS", "NV" ], "options_v3": [ [ "<", ">", ">=", "<=" ], [] ] }, { "id": "Financial_mathematics_0301", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "3", "keywords": [ "algebra" ], "problem_v1": "Find the present value of \\$1377 due after 6 years if the interest rate is $6\\%$ compounded weekly. P=\\$ [ANS]", "answer_v1": [ "960.899698400413" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Find the present value of \\$1041 due after 3 years if the interest rate is $9\\%$ compounded weekly. P=\\$ [ANS]", "answer_v2": [ "794.863540864475" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Find the present value of \\$1157 due after 4 years if the interest rate is $6\\%$ compounded weekly. P=\\$ [ANS]", "answer_v3": [ "910.254364895721" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0302", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "3", "keywords": [ "algebra" ], "problem_v1": "A debt of \\$1800 due in 6 years is to be repaid by a payment of \\$ 500 now and a second payment at the end of 6 years. How much should the second payment be, if the interest rate is 6\\% compounded quarterly? Payment=\\$ [ANS]", "answer_v1": [ "1085.24859403549" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A debt of \\$1260 due in 3 years is to be repaid by a payment of \\$ 500 now and a second payment at the end of 3 years. How much should the second payment be, if the interest rate is 9\\% compounded quarterly? Payment=\\$ [ANS]", "answer_v2": [ "606.975005056216" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A debt of \\$1450 due in 4 years is to be repaid by a payment of \\$ 500 now and a second payment at the end of 4 years. How much should the second payment be, if the interest rate is 6\\% compounded quarterly? Payment=\\$ [ANS]", "answer_v3": [ "815.507226172908" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0303", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "3", "keywords": [ "algebra" ], "problem_v1": "After child's birth, an account has been open, and a single payment has been made, so what when the child is 18, it will receive \\$18000. Find out how much the payment was, if the interest rate is $4\\%$ compounded annually. Payment=\\$ [ANS]", "answer_v1": [ "8885.30617820372" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "After child's birth, an account has been open, and a single payment has been made, so what when the child is 18, it will receive \\$10000. Find out how much the payment was, if the interest rate is $6\\%$ compounded annually. Payment=\\$ [ANS]", "answer_v2": [ "3503.43791129204" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "After child's birth, an account has been open, and a single payment has been made, so what when the child is 18, it will receive \\$13000. Find out how much the payment was, if the interest rate is $4\\%$ compounded annually. Payment=\\$ [ANS]", "answer_v3": [ "6417.16557314713" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0304", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "4", "keywords": [ "percent" ], "problem_v1": "A person has two credit cards with annual interest rates of 16.9 \\% and 18.9 \\% respectively. This month, the total interest for the month due on the balances is $\\\\$302.30$ and the interest due on the first card (at 16.9 \\%) is $\\\\$18.80$ greater than the interest due on the second card. Find the balances on the two cards. Balance on the first card at 16.9 \\%=\\$ [ANS]. Balance on the second card=\\$ [ANS].", "answer_v1": [ "11400", "9000" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "A person has two credit cards with annual interest rates of 10.9 \\% and 12.9 \\% respectively. This month, the total interest for the month due on the balances is $\\\\$164.70$ and the interest due on the first card (at 10.9 \\%) is $\\\\$132.00$ less than the interest due on the second card. Find the balances on the two cards. Balance on the first card at 10.9 \\%=\\$ [ANS]. Balance on the second card=\\$ [ANS].", "answer_v2": [ "1800", "13800" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "A person has two credit cards with annual interest rates of 11.9 \\% and 15.9 \\% respectively. This month, the total interest for the month due on the balances is $\\\\$172.80$ and the interest due on the first card (at 11.9 \\%) is $\\\\$65.70$ less than the interest due on the second card. Find the balances on the two cards. Balance on the first card at 11.9 \\%=\\$ [ANS]. Balance on the second card=\\$ [ANS].", "answer_v3": [ "5400", "9000" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0305", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "4", "keywords": [ "exponential model", "depreciation" ], "problem_v1": "A boat was purchased in early 1991 for \\$23,704. Its value in current dollars depreciates steadily at a rate of 18.9\\% per year.\n(a) What will the boat's value in early 2003? Answer: \\$ [ANS]\n(b) Suppose further that there is 2\\% annual inflation from 1991 to 2003. What will be the value of the boat in early 2003 in inflation-adjusted (early 1991) dollars? Answer: \\$ [ANS]", "answer_v1": [ "1918.98636525602", "1513.10765303862" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "A car was purchased in early 1990 for \\$33,156. Its value in current dollars depreciates steadily at a rate of 11.4\\% per year.\n(a) What will the car's value in early 2009? Answer: \\$ [ANS]\n(b) Suppose further that there is 3.2\\% annual inflation from 1990 to 2009. What will be the value of the car in early 2009 in inflation-adjusted (early 1990) dollars? Answer: \\$ [ANS]", "answer_v2": [ "3325.08572777598", "1827.63134677091" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "A truck was purchased in early 1990 for \\$24,347. Its value in current dollars depreciates steadily at a rate of 13.4\\% per year.\n(a) What will the truck's value in early 2005? Answer: \\$ [ANS]\n(b) Suppose further that there is 7.4\\% annual inflation from 1990 to 2005. What will be the value of the truck in early 2005 in inflation-adjusted (early 1990) dollars? Answer: \\$ [ANS]", "answer_v3": [ "2813.28568267213", "964.161122377002" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0306", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "4", "keywords": [ "interest rate", "loan comparison" ], "problem_v1": "Sara wishes to purchase a stereo system. She is offered the following payment options:\nOption 1: \\$ 0 down \\$ 445 in 1 year \\$ 300 in 2 years\nOption 2: \\$ 95 down \\$ 250 in 1 year \\$ 400 in 2 years\nDetermine the range of interest rates for which the present value of Option 2 is less than the present value of Option 1. Lower limit of range=[ANS]? Upper limit of range=[ANS]?", "answer_v1": [ "0", "0.0526315789473684" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Sara wishes to purchase a stereo system. She is offered the following payment options:\nOption 1: \\$ 0 down \\$ 439 in 1 year \\$ 300 in 2 years\nOption 2: \\$ 80 down \\$ 260 in 1 year \\$ 400 in 2 years\nDetermine the range of interest rates for which the present value of Option 2 is less than the present value of Option 1. Lower limit of range=[ANS]? Upper limit of range=[ANS]?", "answer_v2": [ "0.0787304735160448", "0.158769526483955" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Sara wishes to purchase a stereo system. She is offered the following payment options:\nOption 1: \\$ 0 down \\$ 435 in 1 year \\$ 300 in 2 years\nOption 2: \\$ 85 down \\$ 250 in 1 year \\$ 400 in 2 years\nDetermine the range of interest rates for which the present value of Option 2 is less than the present value of Option 1. Lower limit of range=[ANS]? Upper limit of range=[ANS]?", "answer_v3": [ "0", "0.176470588235294" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0307", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "5", "keywords": [ "annual interest rate" ], "problem_v1": "On January 1, 1998, John deposited \\$ 1000 into Bank X to earn interest at rate i per annum compounded quarterly. On January 1, 2003, he transferred his account to Bank Y to earn interest at rate j per annum compounded semiannually. On January 1, 2006, the balance at Bank Y is \\$ 2252.69. If John could have earned interest at rate j per annum compounded semiannually for the entire eight years, his balance would have been \\$ 2511.27. Calculate the ratio of j to i.\nRatio of j to i=[ANS]?", "answer_v1": [ "1.25418043099848" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "On January 1, 1998, John deposited \\$ 1000 into Bank X to earn interest at rate i per annum compounded bimonthly. On January 1, 2003, he transferred his account to Bank Y to earn interest at rate j per annum compounded quarterly. On January 1, 2006, the balance at Bank Y is \\$ 1583.01. If John could have earned interest at rate j per annum compounded quarterly for the entire eight years, his balance would have been \\$ 1876.25. Calculate the ratio of j to i.\nRatio of j to i=[ANS]?", "answer_v2": [ "1.77171654220521" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "On January 1, 1998, John deposited \\$ 1000 into Bank X to earn interest at rate i per annum compounded bimonthly. On January 1, 2003, he transferred his account to Bank Y to earn interest at rate j per annum compounded quarterly. On January 1, 2006, the balance at Bank Y is \\$ 1813.45. If John could have earned interest at rate j per annum compounded quarterly for the entire eight years, his balance would have been \\$ 2074.39. Calculate the ratio of j to i.\nRatio of j to i=[ANS]?", "answer_v3": [ "1.42663091520565" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0308", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "4", "keywords": [ "future value", "time value of money" ], "problem_v1": "Fund A is invested at an effective annual interest rate of 5\\%. Fund B is invested at an effective annual interest rate of 4.5\\%. At the end of 20 years, the total in the two funds is \\$ 10,000. At the end of 31 years, the amount in Fund A is twice the amount in Fund B. Calculate the total in the two funds at the end of 10 years. Total=[ANS]", "answer_v1": [ "6242.71281706416" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Fund A is invested at an effective annual interest rate of 2\\%. Fund B is invested at an effective annual interest rate of 1.5\\%. At the end of 20 years, the total in the two funds is \\$ 10,000. At the end of 31 years, the amount in Fund A is twice the amount in Fund B. Calculate the total in the two funds at the end of 10 years. Total=[ANS]", "answer_v2": [ "8346.21990692083" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Fund A is invested at an effective annual interest rate of 3\\%. Fund B is invested at an effective annual interest rate of 2.5\\%. At the end of 20 years, the total in the two funds is \\$ 10,000. At the end of 31 years, the amount in Fund A is twice the amount in Fund B. Calculate the total in the two funds at the end of 10 years. Total=[ANS]", "answer_v3": [ "7569.07305612057" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0309", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "3", "keywords": [], "problem_v1": "A bank offers the following certificates of deposit: $\\begin{array}{cc}\\hline Term & Nominal Interest Rate \\\\\\hline(in years) & (compounded semi-annually) \\\\\\hline1 & 5 \\% \\\\\\hline2 & 6 \\% \\\\\\hline3 & 7 \\% \\\\\\hline4 & 8 \\% \\\\\\hline\\end{array}$ The bank requires that interest accumulate at the certificate's interest rate, and does not permit early withdrawal. The certificates mature at the end of the term. During the next six years, the bank will continue to offer these certificates of deposit. Jeff invests \\$ 1500 in the bank. \nCalculate the maximum amount he can withdraw at the end of six years. Maximim after six years=\\$ [ANS]", "answer_v1": [ "2310.5" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A bank offers the following certificates of deposit: $\\begin{array}{cc}\\hline Term & Nominal Interest Rate \\\\\\hline(in years) & (compounded semi-annually) \\\\\\hline1 & 2 \\% \\\\\\hline2 & 3 \\% \\\\\\hline3 & 4 \\% \\\\\\hline4 & 5 \\% \\\\\\hline\\end{array}$ The bank requires that interest accumulate at the certificate's interest rate, and does not permit early withdrawal. The certificates mature at the end of the term. During the next six years, the bank will continue to offer these certificates of deposit. Jeff invests \\$ 2500 in the bank. \nCalculate the maximum amount he can withdraw at the end of six years. Maximim after six years=\\$ [ANS]", "answer_v2": [ "3232.92" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A bank offers the following certificates of deposit: $\\begin{array}{cc}\\hline Term & Nominal Interest Rate \\\\\\hline(in years) & (compounded semi-annually) \\\\\\hline1 & 3 \\% \\\\\\hline2 & 4 \\% \\\\\\hline3 & 5 \\% \\\\\\hline4 & 6 \\% \\\\\\hline\\end{array}$ The bank requires that interest accumulate at the certificate's interest rate, and does not permit early withdrawal. The certificates mature at the end of the term. During the next six years, the bank will continue to offer these certificates of deposit. Jeff invests \\$ 2000 in the bank. \nCalculate the maximum amount he can withdraw at the end of six years. Maximim after six years=\\$ [ANS]", "answer_v3": [ "2742.39" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0310", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "3", "keywords": [ "compound interest", "withdrawal", "penalty" ], "problem_v1": "Carl puts \\$ 10,000 into a bank account that pays an effective annual interest rate of 12\\% for ten years. If withdrawal is made during the first five and one half years, a penalty of 10 \\% of the withdrawal amount is made. Carl withdraws K at the end of each of years 4, 5, 6, and 7. The balance in the account at the end of year 10 is \\$ 10,000. Calculate K\nWithdrawal amount K=\\$ [ANS]", "answer_v1": [ "2970.90917399685" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Carl puts \\$ 10,000 into a bank account that pays an effective annual interest rate of 3\\% for ten years. If withdrawal is made during the first five and one half years, a penalty of 15 \\% of the withdrawal amount is made. Carl withdraws K at the end of each of years 4, 5, 6, and 7. The balance in the account at the end of year 10 is \\$ 10,000. Calculate K\nWithdrawal amount K=\\$ [ANS]", "answer_v2": [ "698.369600487506" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Carl puts \\$ 10,000 into a bank account that pays an effective annual interest rate of 6\\% for ten years. If withdrawal is made during the first five and one half years, a penalty of 10 \\% of the withdrawal amount is made. Carl withdraws K at the end of each of years 4, 5, 6, and 7. The balance in the account at the end of year 10 is \\$ 10,000. Calculate K\nWithdrawal amount K=\\$ [ANS]", "answer_v3": [ "1441.59745801734" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0311", "subject": "Financial_mathematics", "topic": "Interest", "subtopic": "Present and future value of money", "level": "3", "keywords": [ "time value of money", "equation of value" ], "problem_v1": "John is 45 years old. He will receive 2 payments of \\$ 3500 each. The first payment will be an unknown number of years in the future. The second payment will be 7 years after the first payment. At an effective annual rate of interest of 5 \\%, the present value of the two payments is \\$ 4257. Determine at what age John will receive the second payment.(Round to the nearest integer.)\nJohn's age at time of second payment=[ANS] years?", "answer_v1": [ "59" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "John is 20 years old. He will receive 2 payments of \\$ 5000 each. The first payment will be an unknown number of years in the future. The second payment will be 5 years after the first payment. At an effective annual rate of interest of 2 \\%, the present value of the two payments is \\$ 9288. Determine at what age John will receive the second payment.(Round to the nearest integer.)\nJohn's age at time of second payment=[ANS] years?", "answer_v2": [ "26" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "John is 30 years old. He will receive 2 payments of \\$ 3500 each. The first payment will be an unknown number of years in the future. The second payment will be 6 years after the first payment. At an effective annual rate of interest of 3 \\%, the present value of the two payments is \\$ 4112. Determine at what age John will receive the second payment.(Round to the nearest integer.)\nJohn's age at time of second payment=[ANS] years?", "answer_v3": [ "51" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0312", "subject": "Financial_mathematics", "topic": "Options", "subtopic": "Introduction to options", "level": "2", "keywords": [ "financial mathematics", "options" ], "problem_v1": "Suppose that you sell for 5 dollars a call option with a strike price of 55 dollars. If the stock price on the exercise date is 75 dollars, what is your profit? Answer=[ANS] dollars.", "answer_v1": [ "-15" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose that you sell for 2 dollars a call option with a strike price of 65 dollars. If the stock price on the exercise date is 80 dollars, what is your profit? Answer=[ANS] dollars.", "answer_v2": [ "-13" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose that you sell for 3 dollars a call option with a strike price of 55 dollars. If the stock price on the exercise date is 72 dollars, what is your profit? Answer=[ANS] dollars.", "answer_v3": [ "-14" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0313", "subject": "Financial_mathematics", "topic": "Options", "subtopic": "Introduction to options", "level": "3", "keywords": [ "financial mathematics", "options" ], "problem_v1": "Grandpa buys 1000 call options for 4 dollars each, with a strike price of 125 dollars. On the expiration date, the stock price is 155 dollars, and Grandpa's first grandson is born. Grandpa immediately uses the profit from the options to purchase a trust fund for his grandson. The fund will make monthly payments, starting 14 years from now (when Grandpa expects him to begin high school). The payments will increase by 2 dollars each month, and will last forever. Assuming an interest rate of 6.9 percent convertible monthly, what is the amount of the first trust fund payment? Answer=[ANS] dollars.", "answer_v1": [ "41.647562739206" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Grandpa buys 1000 call options for 4 dollars each, with a strike price of 115 dollars. On the expiration date, the stock price is 144 dollars, and Grandpa's first grandson is born. Grandpa immediately uses the profit from the options to purchase a trust fund for his grandson. The fund will make monthly payments, starting 14 years from now (when Grandpa expects him to begin high school). The payments will increase by 2 dollars each month, and will last forever. Assuming an interest rate of 7.2 percent convertible monthly, what is the amount of the first trust fund payment? Answer=[ANS] dollars.", "answer_v2": [ "74.0038343213581" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Grandpa buys 1000 call options for 2 dollars each, with a strike price of 100 dollars. On the expiration date, the stock price is 129 dollars, and Grandpa's first grandson is born. Grandpa immediately uses the profit from the options to purchase a trust fund for his grandson. The fund will make monthly payments, starting 14 years from now (when Grandpa expects him to begin high school). The payments will increase by 4 dollars each month, and will last forever. Assuming an interest rate of 8.4 percent convertible monthly, what is the amount of the first trust fund payment? Answer=[ANS] dollars.", "answer_v3": [ "34.4469222852929" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0314", "subject": "Financial_mathematics", "topic": "Options", "subtopic": "Introduction to options", "level": "3", "keywords": [], "problem_v1": "Suppose a stock is priced at \\$ 65 at expiriry and the annual interest rate is 8 \\%. Determine the profit at expirity for the following one-year european put options:\nA \\$ 60-strike put with premium \\$ 4.3 [ANS]?\nA \\$ 65-strike put with premium \\$ 6.72 [ANS]?\nA \\$ 70-strike put with premium \\$ 9.62 [ANS]?", "answer_v1": [ "0.36", "-7.26", "-10.39" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Suppose a stock is priced at \\$ 25 at expiriry and the annual interest rate is 12 \\%. Determine the profit at expirity for the following one-year european put options:\nA \\$ 20-strike put with premium \\$ 4.94 [ANS]?\nA \\$ 25-strike put with premium \\$ 6.34 [ANS]?\nA \\$ 30-strike put with premium \\$ 9.15 [ANS]?", "answer_v2": [ "-0.53", "-7.1", "-10.25" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Suppose a stock is priced at \\$ 40 at expiriry and the annual interest rate is 8 \\%. Determine the profit at expirity for the following one-year european put options:\nA \\$ 35-strike put with premium \\$ 4.21 [ANS]?\nA \\$ 40-strike put with premium \\$ 6.55 [ANS]?\nA \\$ 45-strike put with premium \\$ 9.28 [ANS]?", "answer_v3": [ "0.45", "-7.07", "-10.02" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Financial_mathematics_0315", "subject": "Financial_mathematics", "topic": "Options", "subtopic": "Introduction to options", "level": "2", "keywords": [], "problem_v1": "The premium of a 100-strike yen-denominated put on the euro is 8.65 Yen. The current exchange rate is 95.65 Yen/euro. What is its premium [ANS] euro?", "answer_v1": [ "0.000904" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "The premium of a 100-strike yen-denominated put on the euro is 8.516 Yen. The current exchange rate is 98.5 Yen/euro. What is its premium [ANS] euro?", "answer_v2": [ "0.000865" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "The premium of a 100-strike yen-denominated put on the euro is 8.562 Yen. The current exchange rate is 95.85 Yen/euro. What is its premium [ANS] euro?", "answer_v3": [ "0.000893" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0316", "subject": "Financial_mathematics", "topic": "Options", "subtopic": "Put-call parity", "level": "3", "keywords": [], "problem_v1": "Suppose the exchange rate is 0.97 \\$/euro, the euro-denominated continuously compounded interest rate is 9\\%, the dollar-denominated continuously compounded interest rate is 4\\%, and the price of a 1-year 0.9675-strike European call on the euro is \\$ 0.0568. What is the price of a 0.9675-strike European put \\$ [ANS]?", "answer_v1": [ "0.099851" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose the exchange rate is 0.9165 \\$/euro, the euro-denominated continuously compounded interest rate is 6\\%, the dollar-denominated continuously compounded interest rate is 6\\%, and the price of a 1-year 0.9365-strike European call on the euro is \\$ 0.0575. What is the price of a 0.9365-strike European put \\$ [ANS]?", "answer_v2": [ "0.076335" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose the exchange rate is 0.935 \\$/euro, the euro-denominated continuously compounded interest rate is 7\\%, the dollar-denominated continuously compounded interest rate is 5\\%, and the price of a 1-year 0.9535-strike European call on the euro is \\$ 0.0567. What is the price of a 0.9535-strike European put \\$ [ANS]?", "answer_v3": [ "0.091909" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0317", "subject": "Financial_mathematics", "topic": "Options", "subtopic": "Put-call parity", "level": "3", "keywords": [], "problem_v1": "Suppose the premium on a 6-month S&R call is \\$ 110.4 and the premium on a put with the same strike price is \\$ 60.6. Assuming that the effective 6-month interest rate is 8 \\%, and that today's price for the S&R index is \\$ 1,000, what is the strike price [ANS]?", "answer_v1": [ "1026.22" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose the premium on a 6-month S&R call is \\$ 112.2 and the premium on a put with the same strike price is \\$ 58.25. Assuming that the effective 6-month interest rate is 2.5 \\%, and that today's price for the S&R index is \\$ 1,000, what is the strike price [ANS]?", "answer_v2": [ "969.7" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose the premium on a 6-month S&R call is \\$ 110.55 and the premium on a put with the same strike price is \\$ 58.9. Assuming that the effective 6-month interest rate is 4.5 \\%, and that today's price for the S&R index is \\$ 1,000, what is the strike price [ANS]?", "answer_v3": [ "991.03" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0318", "subject": "Financial_mathematics", "topic": "Options", "subtopic": "Put-call parity", "level": "4", "keywords": [], "problem_v1": "Suppose the A&T index is 815, the continuously compounded risk-free rate is 6 \\%, and the dividend yield is 0 \\%. A 1-year 829-strike European call costs \\$ 77.05 and a 1-year 829-strike European put cost \\$ 45.65. Consider the strategy of buying the index, selling the 829-strike call, and buying the 829-strike put. What is the continuous rate of return on this position held until the expiration of the options [ANS] \\%?", "answer_v1": [ "5.632" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose the A&T index is 790, the continuously compounded risk-free rate is 3 \\%, and the dividend yield is 0 \\%. A 1-year 815-strike European call costs \\$ 71.65 and a 1-year 815-strike European put cost \\$ 48.5. Consider the strategy of buying the index, selling the 815-strike call, and buying the 815-strike put. What is the continuous rate of return on this position held until the expiration of the options [ANS] \\%?", "answer_v2": [ "6.09" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose the A&T index is 805, the continuously compounded risk-free rate is 3 \\%, and the dividend yield is 0 \\%. A 1-year 818-strike European call costs \\$ 73.5 and a 1-year 818-strike European put cost \\$ 45.85. Consider the strategy of buying the index, selling the 818-strike call, and buying the 818-strike put. What is the continuous rate of return on this position held until the expiration of the options [ANS] \\%?", "answer_v3": [ "5.097" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0319", "subject": "Financial_mathematics", "topic": "Options", "subtopic": "Put-call parity", "level": "3", "keywords": [], "problem_v1": "A stock currently sells for \\$ 33.85. A 6-month call option with strike price of \\$ 30.6 has a premium of \\$ 2.4, and a 6-month put with the same strike has a premium of \\$ 1.2. Assuming a 4 \\% continuously compounded risk-free rate. What is the present value of dividends payable over the next 6 months \\$ [ANS]?", "answer_v1": [ "2.656" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A stock currently sells for \\$ 32.85. A 6-month call option with strike price of \\$ 31.9 has a premium of \\$ 2.13, and a 6-month put with the same strike has a premium of \\$ 1.28. Assuming a 6 \\% continuously compounded risk-free rate. What is the present value of dividends payable over the next 6 months \\$ [ANS]?", "answer_v2": [ "1.043" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A stock currently sells for \\$ 33.4. A 6-month call option with strike price of \\$ 30.4 has a premium of \\$ 2.22, and a 6-month put with the same strike has a premium of \\$ 1.27. Assuming a 5 \\% continuously compounded risk-free rate. What is the present value of dividends payable over the next 6 months \\$ [ANS]?", "answer_v3": [ "2.801" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0320", "subject": "Financial_mathematics", "topic": "Options", "subtopic": "Binomial trees", "level": "3", "keywords": [ "financial mathematics", "binomial trees" ], "problem_v1": "Suppose that a stock price is currently 38 dollars, and it is known that three months from now, the price will be either 46 dollars or 32 dollars. Suppose further that you set up a riskless portfolio that consists of buying 1 European put option with a strike price of 41 dollars, and buying an appropriate number of shares of the stock. Assuming that no arbitrage opportunities exist and a risk-free interest rate of 7.9 percent, what is the value of the riskless portfolio three months before the exercise date? Answer=[ANS] dollars.", "answer_v1": [ "28.9931224281472" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose that a stock price is currently 30 dollars, and it is known that three months from now, the price will be either 36 dollars or 21 dollars. Suppose further that you set up a riskless portfolio that consists of buying 1 European put option with a strike price of 32 dollars, and buying an appropriate number of shares of the stock. Assuming that no arbitrage opportunities exist and a risk-free interest rate of 9.7 percent, what is the value of the riskless portfolio three months before the exercise date? Answer=[ANS] dollars.", "answer_v2": [ "25.767500057293" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose that a stock price is currently 33 dollars, and it is known that three months from now, the price will be either 40 dollars or 27 dollars. Suppose further that you set up a riskless portfolio that consists of buying 1 European put option with a strike price of 35 dollars, and buying an appropriate number of shares of the stock. Assuming that no arbitrage opportunities exist and a risk-free interest rate of 8 percent, what is the value of the riskless portfolio three months before the exercise date? Answer=[ANS] dollars.", "answer_v3": [ "24.1279673429355" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0321", "subject": "Financial_mathematics", "topic": "Options", "subtopic": "Binomial trees", "level": "3", "keywords": [ "financial mathematics", "binomial trees" ], "problem_v1": "Suppose that you buy for 52 dollars a share of stock. In order to hedge your investment, you decide to also buy 2 put options and sell 1 call option on the same stock. Each put costs 6 dollars and has a strike price of 43 dollars. The call costs 4 dollars, and has a strike price of 62 dollars. Find (if it exists) the maximum possible profit for your portfolio on the exercise date. If there is no maximum, then write \"None\" for your answer. (Note: your portfolio contains options and a share of stock.) Answer=[ANS] dollars.", "answer_v1": [ "26" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose that you buy for 56 dollars a share of stock. In order to hedge your investment, you decide to also buy 2 put options and sell 1 call option on the same stock. Each put costs 4 dollars and has a strike price of 35 dollars. The call costs 7 dollars, and has a strike price of 58 dollars. Find (if it exists) the maximum possible profit for your portfolio on the exercise date. If there is no maximum, then write \"None\" for your answer. (Note: your portfolio contains options and a share of stock.) Answer=[ANS] dollars.", "answer_v2": [ "13" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose that you buy for 52 dollars a share of stock. In order to hedge your investment, you decide to also buy 2 put options and sell 1 call option on the same stock. Each put costs 5 dollars and has a strike price of 38 dollars. The call costs 4 dollars, and has a strike price of 59 dollars. Find (if it exists) the maximum possible profit for your portfolio on the exercise date. If there is no maximum, then write \"None\" for your answer. (Note: your portfolio contains options and a share of stock.) Answer=[ANS] dollars.", "answer_v3": [ "18" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0322", "subject": "Financial_mathematics", "topic": "Options", "subtopic": "Binomial trees", "level": "4", "keywords": [], "problem_v1": "Consider an n=1 step binomial tree with T=.5. Suppose r, the annualized risk-free rate is 8 \\%, and delta, the annualized dividend rate is 6 \\%. Also suppose the annualized standard deviation of the continuously compounded stock return, sigma, is 40 \\%. Suppose further that the initial stock price, S=\\$ 110; and that the strike price K is \\$ 103.\na) Determine the European call premium [ANS]?\nb) Determine the European put premium [ANS]?", "answer_v1": [ "18.344", "10.556" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Consider an n=1 step binomial tree with T=.5. Suppose r, the annualized risk-free rate is 12 \\%, and delta, the annualized dividend rate is 11 \\%. Also suppose the annualized standard deviation of the continuously compounded stock return, sigma, is 25 \\%. Suppose further that the initial stock price, S=\\$ 85; and that the strike price K is \\$ 100.\na) Determine the European call premium [ANS]?\nb) Determine the European put premium [ANS]?", "answer_v2": [ "0.835", "14.56" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Consider an n=1 step binomial tree with T=.5. Suppose r, the annualized risk-free rate is 8 \\%, and delta, the annualized dividend rate is 7 \\%. Also suppose the annualized standard deviation of the continuously compounded stock return, sigma, is 30 \\%. Suppose further that the initial stock price, S=\\$ 95; and that the strike price K is \\$ 85.\na) Determine the European call premium [ANS]?\nb) Determine the European put premium [ANS]?", "answer_v3": [ "14.194", "4.129" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0323", "subject": "Financial_mathematics", "topic": "Options", "subtopic": "Hedging strategies", "level": "3", "keywords": [ "financial mathematics", "hedging" ], "problem_v1": "Suppose that you purchase each of the following: for 10 dollars each two calls with a strike price of 49 dollars; for 7 dollars one put with a strike price of 54 dollars; and for 47 dollars a share of the stock. Find the stock price at expiration that will result in the investment breaking even. If there is more than one, give the larger price. Then find (if it exists) the minimum possible profit for your investment on the expiration date. If there is no minimum, then write \"None\" for your answer.\nWhat is the largest stock price at the exercise date that will result in you breaking even? Breakeven stock price=[ANS] dollars. What is the minimum profit possible on the exercise date? Minimum Profit=[ANS] dollars.", "answer_v1": [ "57.3333333333333", "-20" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Suppose that you purchase each of the following: for 7 dollars each two calls with a strike price of 54 dollars; for 5 dollars one put with a strike price of 59 dollars; and for 52 dollars a share of the stock. Find the stock price at expiration that will result in the investment breaking even. If there is more than one, give the larger price. Then find (if it exists) the minimum possible profit for your investment on the expiration date. If there is no minimum, then write \"None\" for your answer.\nWhat is the largest stock price at the exercise date that will result in you breaking even? Breakeven stock price=[ANS] dollars. What is the minimum profit possible on the exercise date? Minimum Profit=[ANS] dollars.", "answer_v2": [ "59.6666666666667", "-12" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Suppose that you purchase each of the following: for 8 dollars each two calls with a strike price of 49 dollars; for 6 dollars one put with a strike price of 54 dollars; and for 47 dollars a share of the stock. Find the stock price at expiration that will result in the investment breaking even. If there is more than one, give the larger price. Then find (if it exists) the minimum possible profit for your investment on the expiration date. If there is no minimum, then write \"None\" for your answer.\nWhat is the largest stock price at the exercise date that will result in you breaking even? Breakeven stock price=[ANS] dollars. What is the minimum profit possible on the exercise date? Minimum Profit=[ANS] dollars.", "answer_v3": [ "55.6666666666667", "-15" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0324", "subject": "Financial_mathematics", "topic": "Options", "subtopic": "Hedging strategies", "level": "3", "keywords": [], "problem_v1": "Consider a bull spread where you buy a \\$ 41-strike call and sell a \\$ 46-strike call. Suppose r=8 \\%, delta(the annualized dividend rate) is 9 \\%, sigma(the annualized standard deviation of the continously compounded stock returns) is 18 \\%, and T=0.5 years. If S=\\$ 43, compute:\na) The net price of the bull spread \\$ [ANS]?\nb) The value of delta [ANS]?\nc) The value of gamma [ANS]?\nd) The value of vega [ANS]?\ne) The value of theta [ANS]?\nf) The value of rho [ANS]?", "answer_v1": [ "2.052673", "0.332965", "0.003038", "0.005055", "0.000593", "0.061324" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [], [] ], "problem_v2": "Consider a bull spread where you buy a \\$ 45-strike call and sell a \\$ 50-strike call. Suppose r=3 \\%, delta(the annualized dividend rate) is 5 \\%, sigma(the annualized standard deviation of the continously compounded stock returns) is 48 \\%, and T=0.5 years. If S=\\$ 35, compute:\na) The net price of the bull spread \\$ [ANS]?\nb) The value of delta [ANS]?\nc) The value of gamma [ANS]?\nd) The value of vega [ANS]?\ne) The value of theta [ANS]?\nf) The value of rho [ANS]?", "answer_v2": [ "0.675597", "0.090644", "0.005718", "0.016811", "-0.001981", "0.012485" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [], [] ], "problem_v3": "Consider a bull spread where you buy a \\$ 41-strike call and sell a \\$ 46-strike call. Suppose r=5 \\%, delta(the annualized dividend rate) is 7 \\%, sigma(the annualized standard deviation of the continously compounded stock returns) is 14 \\%, and T=0.5 years. If S=\\$ 38, compute:\na) The net price of the bull spread \\$ [ANS]?\nb) The value of delta [ANS]?\nc) The value of gamma [ANS]?\nd) The value of vega [ANS]?\ne) The value of theta [ANS]?\nf) The value of rho [ANS]?", "answer_v3": [ "0.371616", "0.176317", "0.05884", "0.059475", "-0.001863", "0.031642" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [], [] ] }, { "id": "Financial_mathematics_0325", "subject": "Financial_mathematics", "topic": "Options", "subtopic": "Hedging strategies", "level": "3", "keywords": [], "problem_v1": "Suppose the oil forward prices for 1 year, 2 years, and 3 years are \\$ 24/barrel, \\$ 25/barrel, and \\$ 26/barrel. The 1-year effective annual interest rate is 8 \\%, the 2-year interest rate is 8.5 \\%, and the 3-year interest rate is 9 \\%.\na) Determine the 3-year swap price \\$ [ANS]?\nb) What is the price of a 2-year swap beginning in one year \\$ [ANS]?", "answer_v1": [ "24.94", "25.476" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Suppose the oil forward prices for 1 year, 2 years, and 3 years are \\$ 20/barrel, \\$ 21/barrel, and \\$ 22/barrel. The 1-year effective annual interest rate is 12 \\%, the 2-year interest rate is 12.5 \\%, and the 3-year interest rate is 13 \\%.\na) Determine the 3-year swap price \\$ [ANS]?\nb) What is the price of a 2-year swap beginning in one year \\$ [ANS]?", "answer_v2": [ "20.916", "21.467" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Suppose the oil forward prices for 1 year, 2 years, and 3 years are \\$ 21.5/barrel, \\$ 22.5/barrel, and \\$ 23.5/barrel. The 1-year effective annual interest rate is 8 \\%, the 2-year interest rate is 8.5 \\%, and the 3-year interest rate is 9 \\%.\na) Determine the 3-year swap price \\$ [ANS]?\nb) What is the price of a 2-year swap beginning in one year \\$ [ANS]?", "answer_v3": [ "22.44", "22.976" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0326", "subject": "Financial_mathematics", "topic": "Options", "subtopic": "Black-Scholes and the Greeks", "level": "3", "keywords": [], "problem_v1": "Consider a perpetual put option with S=\\$ 43, K=\\$ 41, r=8 \\%, delta(the annualized dividend rate) is 9 \\%, sigma(the annualized standard deviation of the continously compounded stock returns) is 18 \\%.\na) What is the price of the perpetual put option \\$ [ANS]?\nb) At what stock price should the perpetual put option be exercised \\$ [ANS]?", "answer_v1": [ "24.9602", "6.8803" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Consider a perpetual put option with S=\\$ 35, K=\\$ 45, r=3 \\%, delta(the annualized dividend rate) is 5 \\%, sigma(the annualized standard deviation of the continously compounded stock returns) is 48 \\%.\na) What is the price of the perpetual put option \\$ [ANS]?\nb) At what stock price should the perpetual put option be exercised \\$ [ANS]?", "answer_v2": [ "7.2121", "27.9527" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Consider a perpetual put option with S=\\$ 38, K=\\$ 41, r=5 \\%, delta(the annualized dividend rate) is 7 \\%, sigma(the annualized standard deviation of the continously compounded stock returns) is 14 \\%.\na) What is the price of the perpetual put option \\$ [ANS]?\nb) At what stock price should the perpetual put option be exercised \\$ [ANS]?", "answer_v3": [ "22.3839", "9.8519" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0327", "subject": "Financial_mathematics", "topic": "Expected and contingent payments", "subtopic": "Contingent payments", "level": "", "keywords": [ "financial mathematics", "contingent payments" ], "problem_v1": "JJ's Bank and Trust would like to obtain a yield of 10 percent on their loans. From past experience, they know that 4.3 percent of loans won't be repaid. What rate of interest should be charged to obtain the desired yield rate on all loans? Answer=[ANS] percent.", "answer_v1": [ "14.9425287356322" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "JJ's Bank and Trust would like to obtain a yield of 8.9 percent on their loans. From past experience, they know that 4.8 percent of loans won't be repaid. What rate of interest should be charged to obtain the desired yield rate on all loans? Answer=[ANS] percent.", "answer_v2": [ "14.390756302521" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "JJ's Bank and Trust would like to obtain a yield of 9.3 percent on their loans. From past experience, they know that 4.4 percent of loans won't be repaid. What rate of interest should be charged to obtain the desired yield rate on all loans? Answer=[ANS] percent.", "answer_v3": [ "14.3305439330544" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0328", "subject": "Financial_mathematics", "topic": "Expected and contingent payments", "subtopic": "Contingent payments", "level": "", "keywords": [ "financial mathematics", "contingent payments" ], "problem_v1": "An investment will pay annual payments of 2100 dollars, the first coming a year from now. The expected yield rate is 9.7 percent effective. Each year there is a 4.5 percent chance that a payment will not be made, and once a payment is missed no further payments are made. If the investment is worth 13454.18 dollars now, how many payments would be made if all payments were received? Answer=[ANS] payments.", "answer_v1": [ "22" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "An investment will pay annual payments of 2500 dollars, the first coming a year from now. The expected yield rate is 9 percent effective. Each year there is a 4 percent chance that a payment will not be made, and once a payment is missed no further payments are made. If the investment is worth 13895.28 dollars now, how many payments would be made if all payments were received? Answer=[ANS] payments.", "answer_v2": [ "11" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "An investment will pay annual payments of 2100 dollars, the first coming a year from now. The expected yield rate is 9.2 percent effective. Each year there is a 4.3 percent chance that a payment will not be made, and once a payment is missed no further payments are made. If the investment is worth 12830.12 dollars now, how many payments would be made if all payments were received? Answer=[ANS] payments.", "answer_v3": [ "15" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0329", "subject": "Financial_mathematics", "topic": "Expected and contingent payments", "subtopic": "Contingent payments", "level": "", "keywords": [ "financial mathematics", "contingent payments" ], "problem_v1": "You have an investment opportunity to receive 1000 dollars at the end of each year for the next 3 years. The probability of receiving the first payment is 0.9, and the probability of receiving the second is 0.81. If the expected yield rate is 10 percent effective, and the expected present value is 2028.54 dollars, what is the probability of receiving the third payment? Answer=[ANS] percent.", "answer_v1": [ "72" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "You have an investment opportunity to receive 1000 dollars at the end of each year for the next 3 years. The probability of receiving the first payment is 0.94, and the probability of receiving the second is 0.76. If the expected yield rate is 8.9 percent effective, and the expected present value is 2030.56 dollars, what is the probability of receiving the third payment? Answer=[ANS] percent.", "answer_v2": [ "68" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "You have an investment opportunity to receive 1000 dollars at the end of each year for the next 3 years. The probability of receiving the first payment is 0.91, and the probability of receiving the second is 0.77. If the expected yield rate is 9.3 percent effective, and the expected present value is 2013.2 dollars, what is the probability of receiving the third payment? Answer=[ANS] percent.", "answer_v3": [ "70" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0330", "subject": "Financial_mathematics", "topic": "Expected and contingent payments", "subtopic": "Contingent payments", "level": "", "keywords": [ "financial mathematics", "contingent payments" ], "problem_v1": "Suppose that MBLA Bank knows that for loans it issues it will either be repaid in full (including interest), repaid exactly half of what is owed (including interest), or repaid nothing at all. MBLA Bank also knows that there is a 15.5 percent chance that it will be repaid exactly half of what is owed, and a 4.3 percent chance that it will be repaid nothing at all. What effective rate of interest should MBLA Bank charge in order to obtain an expected yield rate of 11.3 percent effective? (Note: Assume these loans are to be repaid with a single payment in one year.) Answer=[ANS] percent.", "answer_v1": [ "26.5491756679932" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose that MBLA Bank knows that for loans it issues it will either be repaid in full (including interest), repaid exactly half of what is owed (including interest), or repaid nothing at all. MBLA Bank also knows that there is a 13.6 percent chance that it will be repaid exactly half of what is owed, and a 4.8 percent chance that it will be repaid nothing at all. What effective rate of interest should MBLA Bank charge in order to obtain an expected yield rate of 9.2 percent effective? (Note: Assume these loans are to be repaid with a single payment in one year.) Answer=[ANS] percent.", "answer_v2": [ "23.5294117647059" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose that MBLA Bank knows that for loans it issues it will either be repaid in full (including interest), repaid exactly half of what is owed (including interest), or repaid nothing at all. MBLA Bank also knows that there is a 14.1 percent chance that it will be repaid exactly half of what is owed, and a 4.4 percent chance that it will be repaid nothing at all. What effective rate of interest should MBLA Bank charge in order to obtain an expected yield rate of 9.9 percent effective? (Note: Assume these loans are to be repaid with a single payment in one year.) Answer=[ANS] percent.", "answer_v3": [ "24.1106719367589" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0331", "subject": "Financial_mathematics", "topic": "Expected and contingent payments", "subtopic": "Contingent payments", "level": "", "keywords": [ "financial mathematics", "contingent payments" ], "problem_v1": "Your cousin Vern hits you up for a loan, and tells you that he'll pay you back 1650 dollars a year from now. You'd like an expected yield of 9.7 percent and believe that the likelihood of Vern not paying you back is 4.4 percent. How much should you loan him? Answer=[ANS] dollars.", "answer_v1": [ "1437.92160437557" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Your cousin Vern hits you up for a loan, and tells you that he'll pay you back 1250 dollars a year from now. You'd like an expected yield of 10.2 percent and believe that the likelihood of Vern not paying you back is 3.7 percent. How much should you loan him? Answer=[ANS] dollars.", "answer_v2": [ "1092.33212341198" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Your cousin Vern hits you up for a loan, and tells you that he'll pay you back 1400 dollars a year from now. You'd like an expected yield of 9.7 percent and believe that the likelihood of Vern not paying you back is 3.9 percent. How much should you loan him? Answer=[ANS] dollars.", "answer_v3": [ "1226.43573381951" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0332", "subject": "Financial_mathematics", "topic": "Expected and contingent payments", "subtopic": "Contingent payments", "level": "", "keywords": [ "financial mathematics", "contingent payments" ], "problem_v1": "Suppose that on all loans to be repaid with a single payment in one year, a lending institution charges an effective rate of 11.9 percent, in order to obtain an effective yield of 8 percent. What percentage of loans is the bank assuming will not be repaid? (Note: Assume that the loans will be repaid in full or not at all.) Answer=[ANS] percent.", "answer_v1": [ "3.485254691689" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose that on all loans to be repaid with a single payment in one year, a lending institution charges an effective rate of 12.8 percent, in order to obtain an effective yield of 6.9 percent. What percentage of loans is the bank assuming will not be repaid? (Note: Assume that the loans will be repaid in full or not at all.) Answer=[ANS] percent.", "answer_v2": [ "5.23049645390072" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose that on all loans to be repaid with a single payment in one year, a lending institution charges an effective rate of 12 percent, in order to obtain an effective yield of 7.3 percent. What percentage of loans is the bank assuming will not be repaid? (Note: Assume that the loans will be repaid in full or not at all.) Answer=[ANS] percent.", "answer_v3": [ "4.19642857142859" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0333", "subject": "Financial_mathematics", "topic": "Expected and contingent payments", "subtopic": "Contingent payments", "level": "", "keywords": [ "financial mathematics", "contingent payments" ], "problem_v1": "A credit union makes a loan of 26500 dollars, to be repaid with 12 equal annual payments, the first coming a year from now. They desire a 9.7 percent effective yield on the loan, and estimate that there is a 2.5 percent chance that any given payment will be missed. (However, a missed payment does not change the likelihood of later payments being made.) How much should the annual payments be? Answer=[ANS] dollars.", "answer_v1": [ "3930.51721225731" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A credit union makes a loan of 22500 dollars, to be repaid with 14 equal annual payments, the first coming a year from now. They desire a 9 percent effective yield on the loan, and estimate that there is a 1.9 percent chance that any given payment will be missed. (However, a missed payment does not change the likelihood of later payments being made.) How much should the annual payments be? Answer=[ANS] dollars.", "answer_v2": [ "2945.71497748982" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A credit union makes a loan of 24000 dollars, to be repaid with 12 equal annual payments, the first coming a year from now. They desire a 9.2 percent effective yield on the loan, and estimate that there is a 2.2 percent chance that any given payment will be missed. (However, a missed payment does not change the likelihood of later payments being made.) How much should the annual payments be? Answer=[ANS] dollars.", "answer_v3": [ "3461.61496385895" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0334", "subject": "Financial_mathematics", "topic": "Expected and contingent payments", "subtopic": "Expected payments", "level": "", "keywords": [ "financial mathematics", "expect value" ], "problem_v1": "A game of chance involves rolling a 16-sided die once. If a number from 1 to 3 comes up, you win 3 dollars. If the number 4 or 5 comes up, you win 9 dollars. If any other number comes up, you lose. If it costs 5 dollars to play, what is your expected net winnings? Answer=[ANS] dollars.", "answer_v1": [ "-3.3125" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A game of chance involves rolling a 12-sided die once. If a number from 1 to 3 comes up, you win 4 dollars. If the number 4 or 5 comes up, you win 7 dollars. If any other number comes up, you lose. If it costs 4 dollars to play, what is your expected net winnings? Answer=[ANS] dollars.", "answer_v2": [ "-1.83333333333333" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A game of chance involves rolling a 13-sided die once. If a number from 1 to 3 comes up, you win 3 dollars. If the number 4 or 5 comes up, you win 8 dollars. If any other number comes up, you lose. If it costs 4 dollars to play, what is your expected net winnings? Answer=[ANS] dollars.", "answer_v3": [ "-2.07692307692308" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0335", "subject": "Financial_mathematics", "topic": "Expected and contingent payments", "subtopic": "Expected payments", "level": "", "keywords": [ "financial mathematics", "expect value" ], "problem_v1": "A state lottery sells 57600 tickets. Of these, 1 wins the grand prize which is a perpetuity with equal annual payments of 1600 dollars, with the first payment coming 1 year from now. In addition, 650 other tickets pay a prize of 330 dollars, and 430 tickets pay a prize of 250 dollars. (The rest of the tickets win nothing.) Assuming an effective rate of 6.7 percent for the perpetuity, what is the price of a single ticket so that this is a \"fair\" lottery? Answer=[ANS] dollars.", "answer_v1": [ "6.00487147595357" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A state lottery sells 50800 tickets. Of these, 1 wins the grand prize which is a perpetuity with equal annual payments of 1100 dollars, with the first payment coming 1 year from now. In addition, 570 other tickets pay a prize of 400 dollars, and 430 tickets pay a prize of 210 dollars. (The rest of the tickets win nothing.) Assuming an effective rate of 6 percent for the perpetuity, what is the price of a single ticket so that this is a \"fair\" lottery? Answer=[ANS] dollars.", "answer_v2": [ "6.62664041994751" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A state lottery sells 53100 tickets. Of these, 1 wins the grand prize which is a perpetuity with equal annual payments of 1300 dollars, with the first payment coming 1 year from now. In addition, 610 other tickets pay a prize of 320 dollars, and 440 tickets pay a prize of 280 dollars. (The rest of the tickets win nothing.) Assuming an effective rate of 7.8 percent for the perpetuity, what is the price of a single ticket so that this is a \"fair\" lottery? Answer=[ANS] dollars.", "answer_v3": [ "6.31010671688638" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0336", "subject": "Financial_mathematics", "topic": "Expected and contingent payments", "subtopic": "Expected payments", "level": "", "keywords": [ "financial mathematics", "expect value" ], "problem_v1": "In the Old York State Lottery the probability of winning 75 dollars is 0.37 percent, the probability of winning 820 dollars is 0.043 percent, and the probability of winning 18100 dollars is 0.001 percent. If each ticket costs one dollar and 4 million (i.e. 4000000) tickets will be purchased, what is the total expected profit for Old York? (Note: total expected profit=expected profit per ticket times the number of tickets) Answer=[ANS] dollars.", "answer_v1": [ "755599.999999999" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "In the Old York State Lottery the probability of winning 40 dollars is 0.33 percent, the probability of winning 890 dollars is 0.05 percent, and the probability of winning 15700 dollars is 0.001 percent. If each ticket costs one dollar and 4 million (i.e. 4000000) tickets will be purchased, what is the total expected profit for Old York? (Note: total expected profit=expected profit per ticket times the number of tickets) Answer=[ANS] dollars.", "answer_v2": [ "1064000" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "In the Old York State Lottery the probability of winning 55 dollars is 0.36 percent, the probability of winning 820 dollars is 0.042 percent, and the probability of winning 16400 dollars is 0.001 percent. If each ticket costs one dollar and 4 million (i.e. 4000000) tickets will be purchased, what is the total expected profit for Old York? (Note: total expected profit=expected profit per ticket times the number of tickets) Answer=[ANS] dollars.", "answer_v3": [ "1174400" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0337", "subject": "Financial_mathematics", "topic": "Expected and contingent payments", "subtopic": "Expected payments", "level": "", "keywords": [ "financial mathematics", "expect value" ], "problem_v1": "Suppose that 22 cards, numbered 1 through 22, are placed randomly with faces down on a table. The prize for correctly guessing the value of any given card is 7 dollars. How much should it cost to play in order for this to be a fair game? Answer=[ANS] dollars.", "answer_v1": [ "0.318181818181818" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose that 11 cards, numbered 1 through 11, are placed randomly with faces down on a table. The prize for correctly guessing the value of any given card is 10 dollars. How much should it cost to play in order for this to be a fair game? Answer=[ANS] dollars.", "answer_v2": [ "0.909090909090909" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose that 15 cards, numbered 1 through 15, are placed randomly with faces down on a table. The prize for correctly guessing the value of any given card is 7 dollars. How much should it cost to play in order for this to be a fair game? Answer=[ANS] dollars.", "answer_v3": [ "0.466666666666667" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0338", "subject": "Financial_mathematics", "topic": "Expected and contingent payments", "subtopic": "Expected payments", "level": "", "keywords": [ "financial mathematics", "expect value" ], "problem_v1": "Jeff is producing an outdoor concert. He estimates that he will make 3800 dollars if it does not rain, and make 800 dollars if it does rain. The local weather station (which we'll assume is accurate in giving forecasts) predicts that the chance of rain is 23 percent for the day of the concert. What is Jeff's expected earnings from the concert? Answer=[ANS] dollars.", "answer_v1": [ "3110" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Jeff is producing an outdoor concert. He estimates that he will make 3000 dollars if it does not rain, and make 1000 dollars if it does rain. The local weather station (which we'll assume is accurate in giving forecasts) predicts that the chance of rain is 13 percent for the day of the concert. What is Jeff's expected earnings from the concert? Answer=[ANS] dollars.", "answer_v2": [ "2740" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Jeff is producing an outdoor concert. He estimates that he will make 3300 dollars if it does not rain, and make 800 dollars if it does rain. The local weather station (which we'll assume is accurate in giving forecasts) predicts that the chance of rain is 15 percent for the day of the concert. What is Jeff's expected earnings from the concert? Answer=[ANS] dollars.", "answer_v3": [ "2925" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Financial_mathematics_0339", "subject": "Financial_mathematics", "topic": "Equities", "subtopic": "Introduction to stocks", "level": "2", "keywords": [], "problem_v1": "Suppose a security has a bid price of \\$ 110 and an ask price of \\$ 110.58. At what price can the market-maker purchase the security \\$ [ANS]?\nAt what price can a market-maker sell the security \\$ [ANS]?\nWhat is the spread in dollar terms when 100 shares are traded \\$ [ANS]?", "answer_v1": [ "110", "110.58", "58" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Suppose a security has a bid price of \\$ 83 and an ask price of \\$ 83.93. At what price can the market-maker purchase the security \\$ [ANS]?\nAt what price can a market-maker sell the security \\$ [ANS]?\nWhat is the spread in dollar terms when 100 shares are traded \\$ [ANS]?", "answer_v2": [ "83", "83.93", "93" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Suppose a security has a bid price of \\$ 92 and an ask price of \\$ 92.6. At what price can the market-maker purchase the security \\$ [ANS]?\nAt what price can a market-maker sell the security \\$ [ANS]?\nWhat is the spread in dollar terms when 100 shares are traded \\$ [ANS]?", "answer_v3": [ "92", "92.6", "60" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Financial_mathematics_0340", "subject": "Financial_mathematics", "topic": "Equities", "subtopic": "Introduction to stocks", "level": "3", "keywords": [], "problem_v1": "Suppose you desire to short-sell 400 shares of ABC stock, which has a bid price of \\$ 49.4 and an ask price of \\$ 50.6. You cover the short position 180 days later when the bid price is \\$ 36.84 and the ask price is \\$ 38.04.\na) Taking into account only the bid and ask prices (ignoring commissions and interest), what profit did you make: \\$ [ANS]?\nb) Suppose that there is a 0.3 \\% commission to engage in the short-sale (this is the commission to sell the stock and a 0.3 \\% commission to close the short-sale (this is the commission to buy the stock back). Considering these commissions, what profit did you make: \\$ [ANS]?\nc) Suppose the 6-month interest rate is 3 \\% and that you are paid no interest on the short-sale proceeds. Still assuming that there is a 0.3 \\% commission to engage in the short-sale, how much interest do you lose during the 6 months in which you have the short position: \\$ [ANS]?", "answer_v1": [ "4544", "4439.07", "591.02" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Suppose you desire to short-sell 200 shares of ABC stock, which has a bid price of \\$ 22.1 and an ask price of \\$ 23.9. You cover the short position 180 days later when the bid price is \\$ 17.56 and the ask price is \\$ 19.36.\na) Taking into account only the bid and ask prices (ignoring commissions and interest), what profit did you make: \\$ [ANS]?\nb) Suppose that there is a 0.9 \\% commission to engage in the short-sale (this is the commission to sell the stock and a 0.9 \\% commission to close the short-sale (this is the commission to buy the stock back). Considering these commissions, what profit did you make: \\$ [ANS]?\nc) Suppose the 6-month interest rate is 9 \\% and that you are paid no interest on the short-sale proceeds. Still assuming that there is a 0.9 \\% commission to engage in the short-sale, how much interest do you lose during the 6 months in which you have the short position: \\$ [ANS]?", "answer_v2": [ "548", "473.37", "394.22" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Suppose you desire to short-sell 300 shares of ABC stock, which has a bid price of \\$ 31.4 and an ask price of \\$ 32.6. You cover the short position 180 days later when the bid price is \\$ 24.67 and the ask price is \\$ 25.87.\na) Taking into account only the bid and ask prices (ignoring commissions and interest), what profit did you make: \\$ [ANS]?\nb) Suppose that there is a 0.2 \\% commission to engage in the short-sale (this is the commission to sell the stock and a 0.2 \\% commission to close the short-sale (this is the commission to buy the stock back). Considering these commissions, what profit did you make: \\$ [ANS]?\nc) Suppose the 6-month interest rate is 2 \\% and that you are paid no interest on the short-sale proceeds. Still assuming that there is a 0.2 \\% commission to engage in the short-sale, how much interest do you lose during the 6 months in which you have the short position: \\$ [ANS]?", "answer_v3": [ "1659", "1624.64", "188.02" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Financial_mathematics_0341", "subject": "Financial_mathematics", "topic": "Equities", "subtopic": "Introduction to stocks", "level": "2", "keywords": [], "problem_v1": "XYZ stock has a bid price of \\$ 49.4 and an ask price of \\$ 50.6. Assume there is a \\$ 25 brokerage commission. a) What amount will you pay to buy 100 shares?\nb) What amount will you receive for selling 100 shares?\nc) Suppose you buy 100 shares, immediately sell 100 shares with the bid asn ask prices being the same in both cases. What is you round-trip transaction cost?\nEnter answers here: a) Amount to buy 100 shares=\\$ [ANS]? b) Amount received for 100 shares=\\$ [ANS]? c) Round-trip transaction cost=\\$ [ANS]?", "answer_v1": [ "5085", "4915", "170" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "XYZ stock has a bid price of \\$ 22.1 and an ask price of \\$ 23.9. Assume there is a \\$ 10 brokerage commission. a) What amount will you pay to buy 100 shares?\nb) What amount will you receive for selling 100 shares?\nc) Suppose you buy 100 shares, immediately sell 100 shares with the bid asn ask prices being the same in both cases. What is you round-trip transaction cost?\nEnter answers here: a) Amount to buy 100 shares=\\$ [ANS]? b) Amount received for 100 shares=\\$ [ANS]? c) Round-trip transaction cost=\\$ [ANS]?", "answer_v2": [ "2400", "2200", "200" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "XYZ stock has a bid price of \\$ 31.4 and an ask price of \\$ 32.6. Assume there is a \\$ 15 brokerage commission. a) What amount will you pay to buy 100 shares?\nb) What amount will you receive for selling 100 shares?\nc) Suppose you buy 100 shares, immediately sell 100 shares with the bid asn ask prices being the same in both cases. What is you round-trip transaction cost?\nEnter answers here: a) Amount to buy 100 shares=\\$ [ANS]? b) Amount received for 100 shares=\\$ [ANS]? c) Round-trip transaction cost=\\$ [ANS]?", "answer_v3": [ "3275", "3125", "150" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Financial_mathematics_0342", "subject": "Financial_mathematics", "topic": "Equities", "subtopic": "Forwards and futures", "level": "3", "keywords": [], "problem_v1": "An off-market forward contract is a forward where either you have to pay a premium or you receive a premium for entering into the contract. (With a standard forward contract, the premium is zero.) Suppose the effective annual interest rate is 14 \\% and the S-R index is 1000. Consider 1-year forward contracts.\na) Suppose you are offered a long forward contract at a forward price of \\$ 1290. How much would you need to be paid to enter into this contract \\$ [ANS]?\nb) Suppose you are offered a long forward contract at a forward price of \\$ 1040. How much would you need be willing to pay to enter into this contract \\$ [ANS]?", "answer_v1": [ "131.58", "87.72" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "An off-market forward contract is a forward where either you have to pay a premium or you receive a premium for entering into the contract. (With a standard forward contract, the premium is zero.) Suppose the effective annual interest rate is 3 \\% and the S-R index is 1000. Consider 1-year forward contracts.\na) Suppose you are offered a long forward contract at a forward price of \\$ 1280. How much would you need to be paid to enter into this contract \\$ [ANS]?\nb) Suppose you are offered a long forward contract at a forward price of \\$ 805. How much would you need be willing to pay to enter into this contract \\$ [ANS]?", "answer_v2": [ "242.72", "218.45" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "An off-market forward contract is a forward where either you have to pay a premium or you receive a premium for entering into the contract. (With a standard forward contract, the premium is zero.) Suppose the effective annual interest rate is 7 \\% and the S-R index is 1000. Consider 1-year forward contracts.\na) Suppose you are offered a long forward contract at a forward price of \\$ 1245. How much would you need to be paid to enter into this contract \\$ [ANS]?\nb) Suppose you are offered a long forward contract at a forward price of \\$ 870. How much would you need be willing to pay to enter into this contract \\$ [ANS]?", "answer_v3": [ "163.55", "186.92" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0343", "subject": "Financial_mathematics", "topic": "Equities", "subtopic": "Forwards and futures", "level": "3", "keywords": [], "problem_v1": "A \\$ 90 stock pays \\$ 3.5 every 3 months, with the first dividend coming 3 months from today. The continously compounded risk-free rate is 7 \\%.\na) What is the price of a prepaid forward contract that expires 1 year from today, immediately after the fourth-quarter dividend? \\$ [ANS]? b) What is the price of a forward contract that expires at the same time? \\$ [ANS]?", "answer_v1": [ "76.6", "82.15" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "A \\$ 50 stock pays \\$ 5 every 3 months, with the first dividend coming 3 months from today. The continously compounded risk-free rate is 3 \\%.\na) What is the price of a prepaid forward contract that expires 1 year from today, immediately after the fourth-quarter dividend? \\$ [ANS]? b) What is the price of a forward contract that expires at the same time? \\$ [ANS]?", "answer_v2": [ "30.37", "31.29" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "A \\$ 65 stock pays \\$ 3.5 every 3 months, with the first dividend coming 3 months from today. The continously compounded risk-free rate is 4 \\%.\na) What is the price of a prepaid forward contract that expires 1 year from today, immediately after the fourth-quarter dividend? \\$ [ANS]? b) What is the price of a forward contract that expires at the same time? \\$ [ANS]?", "answer_v3": [ "51.34", "53.44" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0344", "subject": "Financial_mathematics", "topic": "Equities", "subtopic": "Forwards and futures", "level": "3", "keywords": [], "problem_v1": "Suppose the S&P 500 index futures price is currently 1275. You wish to purchase 6 futures contracts on margin.\na) What is the notational value of your postition? \\$ [ANS]? Assuming a 25 \\% initial margin, what is the value of the initial margin? \\$ [ANS]?", "answer_v1": [ "1912500", "478125" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Suppose the S&P 500 index futures price is currently 1075. You wish to purchase 8 futures contracts on margin.\na) What is the notational value of your postition? \\$ [ANS]? Assuming a 10 \\% initial margin, what is the value of the initial margin? \\$ [ANS]?", "answer_v2": [ "2150000", "215000" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Suppose the S&P 500 index futures price is currently 1145. You wish to purchase 6 futures contracts on margin.\na) What is the notational value of your postition? \\$ [ANS]? Assuming a 15 \\% initial margin, what is the value of the initial margin? \\$ [ANS]?", "answer_v3": [ "1717500", "257625" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Financial_mathematics_0345", "subject": "Financial_mathematics", "topic": "Equities", "subtopic": "Forwards and futures", "level": "3", "keywords": [], "problem_v1": "Suppose the A&T index spot price is 1275 and the continuously compounded risk-free rate is 10 \\%. You observe a 8-month forward price of 1277.2. What dividend yield is implied by this forward price? [ANS] \\%?", "answer_v1": [ "9.74" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose the A&T index spot price is 1075 and the continuously compounded risk-free rate is 12 \\%. You observe a 4-month forward price of 1076.45. What dividend yield is implied by this forward price? [ANS] \\%?", "answer_v2": [ "11.6" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose the A&T index spot price is 1150 and the continuously compounded risk-free rate is 10 \\%. You observe a 6-month forward price of 1151.65. What dividend yield is implied by this forward price? [ANS] \\%?", "answer_v3": [ "9.71" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] } ]