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 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 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 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 Present value of an annuity Consider the following cases.     

(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 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 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%.

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 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 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.