| P5–3 Future value You have $100 to invest. If you can earn 12% interest, about how long does it take for your $100 investment to grow to $200? Suppose that the interest |
| rate is just half that, at 6%. At half the interest rate, does it take twice as long to double your money? Why or why not? How long does it take? |
P5-5
| P5–5 Time value You have $1,500 to invest today at 7% interest compounded annually. |
| a. Find how much you will have accumulated in the account at the end of (1) 3 years, (2) 6 years, and (3) 9 years. |
| b. Use your findings in part a to calculate the amount of interest earned in (1) the first 3 years (years 1 to 3), (2) the second 3 years (years 4 to 6), and (3) the third 3 years (years 7 to 9). |
| c. Compare and contrast your findings in part b. Explain why the amount of interest earned increases in each succeeding 3-year period. |
P5-12
| P5–12 Present value concept Answer each of the following questions. |
| a. What single investment made today, earning 12% annual interest, will be worth $6,000 at the end of 6 years? |
| b. What is the present value of $6,000 to be received at the end of 6 years if the discount rate is 12%? |
| c. What is the most you would pay today for a promise to repay you $6,000 at the end of 6 years if your opportunity cost is 12%? |
| d. Compare, contrast, and discuss your findings in parts a through c. |
P5-13
| P5–13 Time value Jim Nance has been offered an investment that will pay him $500 three years from today. |
| a. If his opportunity cost is 7% compounded annually, what value should he place on this opportunity today? |
| b. What is the most he should pay to purchase this payment today? |
| c. If Jim can purchase this investment for less than the amount calculated in part a, what does that imply about the rate of return that he will earn on the investment? |
P5-20
| P5–20 Present value of an annuity Consider the following cases. | |||
| Case | Amount of annuity | Interest rate | Period (years) |
| A | $12,000 | 7% | 3 |
| B | 55,000 | 12 | 15 |
| C | 700 | 20 | 9 |
| D | 140,000 | 5 | 7 |
| E | 22,500 | 10 | 5 |
| a. Calculate the present value of the annuity, assuming that it is | |||
| (1) An ordinary annuity. | |||
| (2) An annuity due. | |||
| b. Compare your findings in parts a(1) and a(2). All else being identical, which type of annuity—ordinary or annuity due—is preferable? Explain why. |
P5-24
| P5–24 Funding your retirement You plan to retire in exactly 20 years. Your goal is to create a fund that will allow you to receive $20,000 at the end of each year for the 30 |
| years between retirement and death (a psychic told you that you would die exactly 30 years after you retire). You know that you will be able to earn 11% per year during |
| the 30-year retirement period. |
| a. How large a fund will you need when you retire in 20 years to provide the 30-year, $20,000 retirement annuity? |
| b. How much will you need today as a single amount to provide the fund calculated in part a if you earn only 9% per year during the 20 years preceding retirement? |
| c. What effect would an increase in the rate you can earn both during and prior to retirement have on the values found in parts a and b? Explain. |
| d. Now assume that you will earn 10% from now through the end of your retirement. You want to make 20 end-of-year deposits into your retirement |
| account that will fund the 30-year stream of $20,000 annual annuity payments. How large do your annual deposits have to be? |
P5-30
| P5–30 Value of mixed streams Find the present value of the streams of cash flows shown in the following table. Assume that the firm’s opportunity cost is 12%. | |||||
| A | B | C | |||
| Year | Cash flow | Year | Cash flow | Year | Cash flow |
| 1 | −$2,000 | 1 | $10,000 | 1−5 | $10,000/yr |
| 2 | 3,000 | 2–5 | 5,000/yr | 6–10 | 8,000/yr |
| 3 | 4,000 | 6 | 7,000 | ||
| 4 | 6,000 | ||||
| 5 | 8,000 |
P5-36
| P5–36 Changing compounding frequency Using annual, semiannual, and quarterly compounding periods for each of the following, (1) calculate the future value if $5,000 is |
| deposited initially, and (2) determine the effective annual rate (EAR). |
| a. At 12% annual interest for 5 years. |
| b. At 16% annual interest for 6 years. |
| c. At 20% annual interest for 10 years. |
P5-43
| P5–43 Creating a retirement fund To supplement your planned retirement in exactly 42 years, you estimate that you need to accumulate $220,000 by the end of 42 years |
| from today. You plan to make equal, annual, end-of-year deposits into an account paying 8% annual interest. |
| a. How large must the annual deposits be to create the $220,000 fund by the end of 42 years? |
| b. If you can afford to deposit only $600 per year into the account, how much will you have accumulated by the end of the forty-second year? |
P5-48
| P5–48 Loan amortization schedule Joan Messineo borrowed $15,000 at a 14% annual rate of interest to be repaid over 3 years. The loan is amortized into three equal, annual, end-of-year payments. |
| a. Calculate the annual, end-of-year loan payment. |
| b. Prepare a loan amortization schedule showing the interest and principal breakdown of each of the three loan payments. |
| c. Explain why the interest portion of each payment declines with the passage of time. |
