Time Value of Money

Problems

1. Future value (LO2) You invest $2,500 a year for three years at 8 percent.

a. What is the value of your investment after one year? Multiply $2,500 × 1.08.

b. What is the value of your investment after two years? Multiply your answer to part a by 1.08.

c. What is the value of your investment after three years? Multiply your answer to part b by 1.08. This gives your final answer.

d. Confirm that your final answer is correct by going to Appendix A (future value of $1), and looking up the future value for n = 3, and i = 8 percent. Multiply this tabular value by $2,500 and compare your answer to the answer in part c. There may be a slight difference due to rounding.

9-1. Solution:

a. $2,500 × 1.08 = $2,700

b. $2,700 × 1.08 = $2,916

c. $2,916 × 1.08 = $3,149.28

d. Appendix A (8%, 3 periods)

FV = PV × FVIF

$2,500 × 1.260 = $3,150

2. Present value (LO3) What is the present value of:

a. $8,000 in 10 years at 6 percent?

b. $16,000 in 5 years at 12 percent?

c. $25,000 in 15 years at 8 percent?

Solution:

3. Present Value (LO3)

a. What is the present value of $100,000 to be received after 40 years with an 18 percent discount rate?

b. Would the present value of the funds in part be enough to buy a $125 concert ticket?

Solution:

Appendix B

PV = FV × PVIF (18%, 40 periods)

a. $100,000 × .001 = $100

b. NO. You only have $100 in present value.

4. Present Value (LO4) You will receive $4,000 three years from now. The discount rate is 10 percent.

a. What is the value of your investment two years from now? Multiply $4,000 × .909 (one year’s discount rate at 10 percent).

b. What is the value of your investment one year from now? Multiply your answer to part a by .909 (one year’s discount rate at 10 percent).

c. What is the value of your investment today? Multiply your answer to part b by .909 (one year’s discount rate at 10 percent).

d. Confirm that your answer to part c is correct by going to Appendix B (present value of $1) for n = 3 and i = 10%. Multiply this tabular value by $4,000 and compare your answer to part c. There may be a slight difference due to rounding.

9-4. Solution:

5. Future value (LO2) If you invest $12,000 today, how much will you have:

a. In 6 years at 7 percent?

b. In 15 years at 12 percent?

c. In 25 years at 10 percent?

d. In 25 years at 10 percent (compounded semiannually)?

9-5. Solution:

Appendix A

FV = PV × FVIF

a. $12,000 × 1.501 = $ 18,012

b. $12,000 × 5.474 = $ 65,688

c. $12,000 × 10.835 = $130,020

d. $12,000 × 11.467 = $137,604 (5%, 50 periods)

6. Present value (LO3) Your aunt offers you a choice of $20,000 in 50 years or $45 today. If money is discounted at 13 percent, which should you choose?

9-6. Solution:

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