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Present and Future Values

1. Present Values. Compute the present value of a $100 cash flow for the following combinations of discount rates and times:

a. r = 10 percent. t = 10 years

b. r = 10 percent. t = 20 years

c. r = 5 percent. t = 10 years

d. r = 5 percent. t = 20 years

2. Future Values. Compute the future value of a $100 cash flow for the same combinations of rates and times as in problem 1.

3. Future Values. In 1880 five aboriginal trackers were each promised the equivalent of 100 Australian dollars for helping to capture the notorious outlaw Ned Kelley. In 1993 the granddaughters of two of the trackers claimed that this reward had not been paid. The Victorian prime minister stated that if this was true, the government would be happy to pay the $100. However, the granddaughters also claimed that they were entitled to compound interest. How much was each entitled to if the interest rate was 5 percent? What if it was 10 percent?

4. Future Values. You deposit $1,000 in your bank account. If the bank pays 4 percent simple interest, how much will you accumulate in your account after 10 years? What if the bank pays compound interest? How much of your earnings will be interest on interest?

5. Present Values. You will require $700 in 5 years. If you earn 6 percent interest on your funds, how much will you need to invest today in order to reach your savings goal?

6. Calculating Interest Rate. Find the interest rate implied by the following combinations of present and future values:

Present Value Years Future Value

$400 11 $684

$183 4 $249

$300 7 $300 7. Present Values. Would you rather receive $1,000 a year for 10 years or $800 a year for 15 years if

a. the interest rate is 5 percent?

b. the interest rate is 20 percent?

c. Why do your answers to (a) and (b) differ?

8. Calculating Interest Rate. Find the annual interest rate.

Present Value Future Value Time Period

100 115.76 3 years

200 262.16 4 years

100 110.41 5 years

9. Present Values. What is the present value of the following cash-flow stream if the interest rate is 5 percent?

Year Cash Flow

1 $200

2 $400

3 $300

10. Number of Periods. How long will it take for $400 to grow to $1,000 at the interest rate specified?

a. 4 percent

b. 8 percent

c. 16 percent

11. Calculating Interest Rate. Find the effective annual interest rate for each case: APR Compounding Period

12% 1 month

8% 3 months

10% 6 months

12. Calculating Interest Rate. Find the APR (the stated interest rate) for each case: Effective Annual Compounding Interest Rate Period

10.00% 1 month

6.09% 6 months

8.24% 3 months

13. Growth of Funds. If you earn 8 percent per year on your bank account, how long will it take an account with $100 to double to $200?

14. Comparing Interest Rates. Suppose you can borrow money at 8.6 percent per year (APR) compounded semiannually or 8.4 percent per year (APR) compounded monthly. Which is the better deal?

15. Calculating Interest Rate. Lenny Loanshark charges ¬one point ­ per week (that is, 1 percent per week) on his loans. What APR must he report to consumers? Assume exactly 52 weeks in a year. What is the effective annual rate?

16. Compound Interest. Investments in the stock market have increased at an average compound rate of about 10 percent since 1926.

a. If you invested $1,000 in the stock market in 1926, how much would that investment be

worth today?

b. If your investment in 1926 has grown to $1 million, how much did you invest in 1926?

17. Compound Interest. Old Time Savings Bank pays 5 percent interest on its savings accounts. If you deposit $1,000 in the bank and leave it there, how much interest will you earn in the first year? The second year? The tenth year?

18. Compound Interest. New Savings Bank pays 4 percent interest on its deposits. If you deposit $1,000 in the bank and leave it there, will it take more or less than 25 years for your money to double? You should be able to answer this without a calculator or interest rate tables.

19. Calculating Interest Rate. A zero-coupon bond which will pay $1,000 in 10 years is selling today for $422.41. What interest rate does the bond offer?

20. Present Values. A famous quarterback just signed a $15 million contract providing $3 million a year for 5 years. A less famous receiver signed a $14 million 5-year contract providing $4 million now and $2 million a year for 5 years. Who is better paid? The interest rate is 12 percent.