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Chapter 3 The Time Value of Money
4. You need to have $50,000 at the end of 10 years. To accumulate this sum, you have decided to save a certain amount at the end of each of the next 10 years and deposit it in the bank. The bank pays 8 percent interest compounded annually for long-term deposits. How much will you have to save each year (to the nearest dollar)?
5. Same as Problem 4 above, except that you deposit a certain amount at the beginning of each of the next 10 years. Now, how much will you have to save each year (to the nearest dollar)?
9. The H & L Bark Company is considering the purchase of a debarking machine that is expected to provide cash flows as follows:
| |END OF YEAR |
| |1 |2 |3 |4 |5 |
|Cash flow |$1,200 |$2,000 |$2,400 |$1,900 |$1,600 |
| |END OF YEAR |
| |6 |7 |8 |9 |10 |
|Cash flow |$1,400 |$1,400 |$1,400 |$1,400 |$1,400 |
If the appropriate annual discount rate is 14 percent, what is the present value of this cash-flow stream?
14. Establish loan amortization schedules for the following loans to the nearest cent (see Table 3.8 for an example):
a. A 36-month loan of $8,000 with equal installment payments at the end of each month. The interest rate is 1 percent per month.
b. A 25-year mortgage loan of $184,000 at a 10 percent compound annual interest rate with equal installment payments at the end of each year.
15. You have borrowed $14,300 at a compound annual interest rate of 15 percent. You feel that you will be able to make annual payments of $3,000 per year on your loan. (Payments include both principal and interest.) How long will it be before the loan is entirely paid off (to the nearest year)?
17. Earl E. Bird has decided to start saving for his retirement. Beginning on his twenty-first birthday, Earl plans to invest $2,000 each birthday into a savings investment earning a 7 percent compound annual rate of interest. He will continue this savings program for a total of 10 years and then stop making payments. But his savings will continue to compound at 7 percent for 35 more years, until Earl retires at age 65. Ivana Waite also plans to invest $2,000 a year, on each birthday, at 7 percent, and will do so for a total of 35 years. However, she will not begin her contributions until her thirty-first birthday. How much will Earl's and Ivana's savings programs be worth at the retirement age of 65? Who is better off financially at retirement, and by how much?
20. Suppose that an investment promises to pay a nominal 9.6 percent annual rate of interest. What is the effective annual interest rate on this investment assuming that interest is compounded (a) annually? (b) semiannually? (c) quarterly? (d) monthly? (e) daily (365 days)? (f) continuously? (Note: Report your answers accurate to four decimal places - e.g., 0.0987 or 9.87%.)
22. It took roughly 14 years for the Dow Jones Average of 30 Industrial Stocks to go from 1,000 to 2,000. To double from 2,000 to 4,000 took only 8 years, and to go from 4,000 to 8,000 required roughly 2 years. To the nearest whole percent, what compound annual growth rates are implicit in these three index-doubling milestones?
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