Compound Interest Practice Problems

[Pages:3]University of Virginia - math1140: Financial Mathematics

Fall 2011

Compound Interest Practice ProblemsOctober 20, 2011

Some of these problems were created by Professor Jeff Holt for a previous version of this class. Some of these problems are from the textbook.

Problem 1. Dave invests $2800 at 8% annual interest compounded once per year. How much does he have in 7 years?

Problem 2. Jack deposits $7, 000 in an account paying 2.1% interest per quarter, compounded 4 times per year. What is the account balance after 6 years?

Problem 3. Carrie invests $3, 500 in an account paying an interest rate of i per month, compounded monthly. In 7 years she has doubled her money. What is the rate of interest i?

Problem 4. Alice borrows $2, 250 at an interest rate of 4.7% per 6 months, compounded twice annually. How much does she owe 5 years and 7 months later?

Problem 5. Bob opens a savings account with a deposit of $800. Two years later, he deposits another $650. If the account pays an annual interest rate of 6.1% compounded once per year, what is the account balance 5 years after the initial deposit?

Problem 6. Roland opens an investment account on January 1 with a deposit of $2, 000. He makes another deposit of $2, 000 at the beginning of each of the following three quarters (Apr. 1, July 1, Oct. 1). If the investment pays 2.7% interest per quarter, compounded quarterly, how much is the investment worth a year after the account is opened?

Problem 7. Carolyn loans her brother Dave $100 at the beginning of January. At the beginning of March, she loans him another $85. At the beginning of July, he repays her $120. At the beginning of September, he borrows another $60. If Carolyn charges 0.85% interest per month compounded monthly, how much does Dave owe her at the beginning of December?

Problem 8. Suppose that you purchase the deluxe George Foreman grill system for $200, and charge it on your credit card. If the card charges you 1.6% interest monthly, how much will you owe in one year? (Assume, unrealistically, that no payments are made during the year and no fees are charged for not paying the minimum payment.) What is the nominal interest rate?

Problem 9. Suppose that $45, 000 is invested at a nominal rate of 7% convertible quarterly. What is the investment worth in 5 years?

Problem 10. A savings account pays a nominal rate of 7.2% convertible monthly. What is the monthly interest rate?

Problem 11. An account pays a nominal rate of 4.5% convertible daily. How much must be invested to have $5, 000 a year later?

Problem 12. $8000 is deposited in a savings account that pays interest convertible monthly. Two years later, the account balance is $9700. What is the nominal interest rate?

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Problem 13. Suppose that Ed invests $1, 000 at the beginning of 1993, and adds another $2, 000 to the investment at the beginning of 1996. If the nominal rate of interest is 8% convertible quarterly, what is the future value of the investment at the beginning of 2005?

Problem 14. Suppose that Ed invests $1000 at the beginning of 1993, and adds another $2000 to the investment at the beginning of 1996. If the nominal rate of interest is 8% convertible quarterly, what is the present value of the investment at the beginning of 1985?

Problem 15. Homer wins $100, 000, 000 in the lottery, to be paid out in 25 annual installments of $4, 000, 000 each, with the first payment coming immediately. What is the present value of the final payment, assuming an effective rate of 8.7%?

Problem 16. Bart has an investment that will pay him $2, 000 in one year, and another $4, 000 in three years. What is the present value of Barts investment, assuming 12.1% effective interest?

Problem 17. On January 1, 1995, Maggie received a payment of $2, 500. On January 1, 2005, she will receive another payment of $5, 000. On January 1, 2015, she will receive a final payment of $10, 000. If we assume a nominal rate of 7% convertible semiannually, what is the present value of all of these payments on January 1, 2002?

Problem 18. Justine would like to have $20, 000 in a savings account 10 years from now. She plans to reach her goal by making a deposit now and another in 4 years. If the first deposit is twice the amount of the second and the account pays an nominal rate of 7% compounded yearly, how large is the first deposit?

Problem 19. Suppose that you establish a line of credit that charges a nominal rate of 12.3% convertible monthly, and immediately borrow $1300. 9 months later, you borrow another $950. 5 months after that, you make a payment of X dollars. Two years after opening the line of credit, you owe the bank $1150. What is X?

Problem 20. You have the opportunity to invest in the company that produces Hairigomi, the hair-care wonder. The investment promises to pay a return of 23% compounded annually. How long will it take for $10, 000 to grow into $70, 000? (Assume compound interest at all times.)

Problem 21. Consider two investments: the first involves depositing $1, 000 in an account paying a nominal rate of 5% convertible monthly, and the second involves depositing $800 in an account paying an effective rate of 6%. How long will it take for the two accounts to have the same balance? (Assume compound interest at all times.)

Problem 22. Mary Ann deposits $8, 000 in a savings account paying a nominal rate of 5.2% convertible quarterly. Two years later, she withdraws $2, 500. If there are no other transactions, how long will it take from the time of the original deposit for the account balance to reach $11, 000? (Assume simple interest between compoundings.)

Problem 23. Bill invests $1, 000 in an account paying interest convertible annually, and another $2, 000 in the account a year later. If the account is worth $3, 600 in two years, what is the effective rate of interest?

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Problem 24. Kelly puts $6, 500 into a mutual fund on January 1, 1994. She puts another $8, 000 into the same fund on January 1, 1997. On January 1, 2000, her fund balance is $18, 000. What was her effective rate of interest? Problem 25. Which is higher: a) 7.2%(1) or 7%(4) b) 7.2%(2) or 7%(12) c) 12%(12) or 12.3%(4) d) 12%(12) or 12.3%(2)

Problem 26. How much more additional interest would you get on $10, 000 for 3 years if money is worth 8%(4) instead of 8%(2)? Problem 27. How much more additional interest would you get on $100, 000 for 3 years if money is worth 6%(12) instead of 6%(1)? Problem 28. A $2, 000, 8%(2) matures in 3 years. In 2 years it is sold to a thitd party who requires 6%(4) on his money. Find the purchase price, and the return on the investment of the original owner. Problem 29. A $4, 000, 2-year note is sold in one year to a person requiring 7% on his money. Find the proceeds. Problem 30. Find the NPV at 20%(1) and 30%(1) for an investment costing $5, 00 now and returning $400 in one year and $300 in two. Problem 31. A father deposits $7, 000 on his son tenth birthday into an education money market fund that has a yield rate of 7%(2). The fund is to be distributed in two equal amounts on the son's 20th and 21st birthdays. Find the two equal amounts.

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