2.2 Compound Interest
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1 2.2 Compound Interest TRUE/FALSE 1. Doubling the frequency of compounding in a compound interest investment will not double the amount of the interest. ANS: T MSC: wcfm The effective rate exceeds the nominal rate when the interest is compounded less than once a year resulting in a larger effective rat ANS: F MSC: wcfm MULTIPLE CHOICE 1. Calculate the future value of an investment of $3,000, after one year, if it is deposited in a savings account that is compounded quarterly at an annual rate of 12%. $3, $3, c. $3, d. $3, ANS: C MSC: wcfm m 2. $10,000 is deposited in a money market account when interest is compounded every month at an annual rate of 11%. Find the total amount accumulated at the end of 6 years. Round your answer to the nearest cent. $19, $72, c. $17, d. $19, ANS: A MSC: wcfm m 3. You invest $10,000 in Rapid Growth Funds, which appreciate by 4%/year, with yields reinvested quarterly. By how much will your investment have grown after 7 years? Round your answer to the nearest cent. $19, $3, c. $3, d. $ ANS: E MSC: wcfm m 4. How much would you have to invest when you are 22 years old at 7% compounded monthly to end up with a million dollars by age 52? Round your answer to the nearest thousand.
2 $213,000 $131,000 c. $215,000 d. $123,000 ANS: D MSC: wcfm m 5. Calculate, to the nearest 0.1%, what annual interest rate would be required if you invested $6,000 in Apple stock and ended up with $13,415 when you sold the stock after 12 years? Assume that interest was compounded quarterly. 7.2% 7.4% c. 6.8% d. 6.6% ANS: C MSC: wcfm m 6. Inflation has been running 2%/year. A car now costs $37,000. How much would it have cost 6 years ago? $32, $33, c. $32, d. $32, ANS: A MSC: wcfm m 7. Find the effective annual interest rate of 5% compounded quarterly. 5.34% 5.25% c. 5.09% d. 5.39% ANS: C MSC: wcfm m 8. You are offered three investments. What is the best investment? The second will earn 18.5% compounded quarterly. The third will earn 18% compounded weekly. c. The first promises to earn 19% compounded annually. ANS: A MSC: wcfm m 9. Calculate the future value of an investment of $11,000 at 1.5%/year, compounded weekly, after 2 years. Assume 52 weeks per year. $10, $11,206.80
3 c. $10, d. $11, ANS: D MSC: wcfm m 10. Calculate the future value of an investment of $7,000 at 0.2%/year, compounded monthly, after 2 years. $7, $7, c. $7, d. $7, $6, ANS: A MSC: wcfm m 11. Calculate the present value of an investment that will be worth $4,000 after 3 years at 7%/year compounded annually. $3, $3, c. $3, d. $2, $3, ANS: B MSC: wcfm m 12. Find the effective annual interest rate of 17% compounded monthly. c. d. ANS: D MSC: wcfm m 13. Determine the amount of money, to the nearest dollar, you must invest now at 4%/year compounded annually, so that you will be a millionaire in 55 years. Round your answer to the nearest dollar. $115,656 $124,420 c. $111,209 d. $110,255 $112,129 ANS: A MSC: wcfm m 14. Calculate, to the nearest cent, the future value of an investment of $11,000 at 4.5% per year, compounded quarterly ( 4 times / year ), after 10 years. c.
4 d. ANS: D MSC: wcfm m 15. Calculate, to the nearest cent, the future value of an investment of $28,000 at 10.75% per year, compounded monthly, after 15 years. c. d. ANS: C MSC: wcfm m 16. Calculate, to the nearest cent, the present value of an investment that will be worth $3,000 after 16 years, at 5% per year, compounded annually. c. d. ANS: B MSC: wcfm m 17. Calculate, to the nearest cent, the present value of an investment that will be worth $10,000 after 6 years, at 6.2% compounded quarterly. c. d. ANS: E MSC: wcfm m 18. Find the effective annual interest rate of 11% compounded monthly. Round your answer to the nearest 0.01%. c. d. ANS: A MSC: wcfm m 19. Find the effective annual interest rate of 15% compounded daily. Assume 365 days per year. Round your answer to the nearest 0.01%.
5 c. d. ANS: B MSC: wcfm m 20. You deposit $500 in an account at the Lifelong Trust Savings and Loan that pays 4%/year compounded quarterly. By how much will your deposit have grown after 4 years? Round the answer to the nearest cent. $ $ c. $86.29 d. $86.19 $83.19 ANS: C MSC: wcfm m 21. When I was considering what to do with my $10,500 Lottery winnings, my broker suggested I invest half of it in gold, whose value was growing by 14%/year, and the other half in certificates of deposit (CDs), which were yielding 6%/year compounded every 6 months. Assuming that these rates are sustained, how much will my investment be worth in 13 years? Round your answer to the nearest cent. $23, $40, c. $42, d. $40, $43, ANS: D MSC: wcfm m 22. When I was considering what to do with the $3,500 proceeds from my sale of technology stock, my broker suggested I invest half of it in municipal bonds, whose value was growing by 11%/year, and the other half in certificates of deposit (CDs), which were yielding 8%/year compounded every 2 months. Assuming that these rates are sustained, how much will my investment be worth in 12 years? Round your answer to the nearest cent. $4, $10, c. $6, d. $10, $10, ANS: B MSC: wcfm m 23. During a prolonged recession, property values on Long Island depreciated by 8% every six months. If my house cost $240,000 originally, how much was it worth 7 years later? Round your answer to the nearest cent. $74, $74, c. $74, d. $74, $74,687.28
6 ANS: D MSC: wcfm m 24. My recent marketing idea, the Miracle Algae Growing Kit, has been remarkably successful, with monthly sales growing by 4% every 6 months over the past 4 years. Assuming that I sold 400 kits the first month, what is the present rate of sales? Round your answer to the nearest whole number. 433 kits per month 432 kits per month c. 470 kits per month d. 547 kits per month 469 kits per month ANS: D MSC: wcfm m 25. Inflation is running at 2.4% per year when you deposit $12,000 in an account earning 6.3% per year compounded quarterly. In constant dollars, how much money will you have 7 years from now? Round your answer to the nearest cent. [Hint: First calculate the value of your account in 7 year's time, and then find its present value based on the inflation rat] $15, $15, c. $15, d. $15, $15, ANS: A MSC: wcfm m 26. If Brazil has an annual inflation rate of 11% and an item will cost 150,000 in 4 years, what does the same item cost now? Round to the nearest. 98,820 98,815 c. 230,203 d. 98, ,440 ANS: D MSC: wcfm m 27. The nominal rate exceeds the effective rate when the interest is compounded once a year resulting in a larger effective rat equally less or equally than c. more or equally than d. less than more than ANS: D MSC: wcfm m 28. Doubling the frequency of compounding in a compound interest investment double the amount of the interest. will will not
7 ANS: B MSC: wcfm m NUMERIC RESPONSE 1. Find the effective annual interest rate of 8% compounded monthly. Round your answer to the nearest 0.01%. ANS: 8.30 = % MSC: wcfm Calculate, to the nearest cent, the future value of an investment of $18,000 at 5% per year, compounded annually, after 11 years. ANS: 30, MSC: wcfm Calculate, to the nearest cent, the future value of an investment of $15,000 at 4.25% per year, compounded quarterly, after 5 years. ANS: 18, MSC: wcfm Calculate, to the nearest cent, the future value of an investment of $26,000 at 7% per year, compounded monthly, after 18 years. ANS: 91, MSC: wcfm Calculate, to the nearest cent, the present value of an investment that will be worth $3,000 after 8 years, at 11% per year, compounded annually. ANS: 1, MSC: wcfm Calculate, to the nearest cent, the present value of an investment that will be worth $10,000 after 9 years, at 8% compounded monthly.
8 ANS: 4, MSC: wcfm Find the effective annual interest rate of 9% compounded monthly. Round your answer to the nearest 0.01%. ANS: 9.38 % MSC: wcfm Find the effective annual interest rate of 11% compounded daily. Assume 365 days per year. Round your answer to the nearest 0.01%. ANS: % MSC: wcfm When I was considering what to do with my $10,500 Lottery winnings, my broker suggested I invest half of it in gold, whose value was growing by 11%/year, and the other half in certificates of deposit (CDs), which were yielding 6%/year compounded every 6 months. Assuming that these rates are sustained, how much will my investment be worth in 11 years? Round your answer to the nearest cent. ANS: 26, MSC: wcfm When I was considering what to do with the $4,500 proceeds from my sale of technology stock, my broker suggested I invest half of it in municipal bonds, whose value was growing by 8%/year, and the other half in certificates of deposit (CDs), which were yielding 9%/year compounded every 2 months. Assuming that these rates are sustained, how much will my investment be worth in 9 years? Round your answer to the nearest cent. ANS: 9, MSC: wcfm You invest $5,000 in Rapid Growth Funds, which appreciate by 7% per year, with yields reinvested quarterly. By how much will your investment have grown after 6 years? Round your answer to the nearest cent.
9 ANS: 2, MSC: wcfm During a prolonged recession, property values on Long Island depreciated by 4% every six months. If my house cost $140,000 originally, how much was it worth 9 years later? Round your answer to the nearest cent. ANS: 97, MSC: wcfm Determine the amount of money, to the nearest dollar, you must invest at 6.2% per year, compounded semiannually, so that you will be a millionaire in 24 years tim Round your answer to the nearest dollar. ANS: 230,985 MSC: wcfm My recent marketing idea, the Miracle Algae Growing Kit, has been remarkably successful, with monthly sales growing by 4% every 6 months over the past 8 years. Assuming that I sold 400 kits the first month, what is the present rate of sales? Round your answer to the nearest whole number. kits per month ANS: 549 MSC: wcfm Inflation is running at 2.6% per year when you deposit $15,000 in an account earning 6.1% per year compounded quarterly. In constant dollars, how much money will you have 6 years from now? Round your answer to the nearest cent. [Hint: First calculate the value of your account in 6 year's time, and then find its present value based on the inflation rat] ANS: 18, MSC: wcfm If Brazil has an annual inflation rate of 11% and an item will cost 145,000 in 3 years, what does that same item cost now? Round to the nearest. ANS: 106,023 MSC: wcfm
10 17. Calculate, to the nearest cent, the future value of an investment of $13,000 at 1.5%/year, compounded quarterly, after 4 years. ANS: 13, MSC: wcfm Calculate, to the nearest cent, the future value of an investment of $6,000 at 5.5%/year, compounded weekly, after 6 years. Assume 52 weeks per year. ANS: 8, MSC: wcfm Calculate, to the nearest cent, the future value of an investment of $15,000 at 0.4%/year, compounded monthly, after 5 years. ANS: 15, MSC: wcfm Calculate the present value of an investment that will be worth $3,000 after 4 years at 3%/year compounded annually. Round your answer to the nearest cent. ANS: 2, MSC: wcfm You deposit $500 in an account at the Lifelong Trust Savings and Loan that pays 4%/year compounded quarterly. By how much will your deposit have grown after 4 years? Round the answer to the nearest cent. $ ANS: MSC: wcfm Determine the amount of money, to the nearest dollar, you must invest now at 5%/year compounded annually, so that you will be a millionaire in 50 years. Round your answer to the nearest cent. $ ANS: 87,203.73
11 MSC: wcfm Calculate, to the nearest cent, the future value of an investment of $13,000 at 0.4% per month, compounded monthly, after 9 years. ANS: 20, MSC: wcfm Inflation has been running 2%/year. A car now costs $32,000. How much would it have cost 9 years ago? Round your answer to the nearest cent. The car will have cost 9 years ago. ANS: 26, MSC: wcfm Calculate, to the nearest 0.1%, what annual interest rate would be required if you invested $4,000 in Apple stock and ended up with $11,027 when you sold the stock after 9 years? Assume that interest was compounded quarterly. The required annual interest rate is %. ANS: 11.4 MSC: wcfm SHORT ANSWER 1. Find the effective annual interest rate of 5%/year compounded annually, semiannually, quarterly, and monthly. Round the answers to 0.01%. nominal rate compound annually nominal rate compound semiannually nominal rate compound quarterly nominal rate compound monthly %/year %/year %/year %/year ANS: ; ; ; MSC: wcfm You are offered three investments. The first promises to earn 19% compounded annually, the second will earn 18.5% compounded quarterly, and the third will earn 18% compounded weekly. What is the best investment? The best investment is the investment. ANS:
12 second MSC: wcfm
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