Exam 5: Time Value of Money

Bill plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 20 years. If Bill can earn 12 percent on his contributions, how much will he have at the end of the twentieth year?

The effective annual rate increases with increasing compounding frequency.

Last Christmas, Danny received an annual bonus of $1,500. These annual bonuses are expected to grow by 5 percent for the next 5 years. How much will Danny have at the end of the fifth year if he invests his Christmas bonuses (including the most recent bonus) in a project paying 8 percent per year?

Nancy would like to accumulate $10,000 by the end of 3 years from now to buy a sports car from her friend, Jim. She has $2,500 now and would like to save equal annual end-of-year deposits to pay for the car. How much should she deposit at the end of each year in an account paying 8 percent interest to buy the car?

To buy his favorite car, Larry is planning to accumulate money by investing his Christmas bonuses for the next five years in a security which pays a 10 percent annual rate of return. The car will cost $20,000 at the end of the fifth year and Larry's Christmas bonus is $3,000 a year. Will Larry accumulate enough money to buy the car?

In general, with an amortized loan, the payment amount remains constant over the life of the loan, the principal portion of each payment grows over the life of the loan, and the interest portion of each payment declines over the life of the loan.

When computing an interest or growth rate, the rate will increase with an increase in future value, holding present value and the number of periods constant.

Timothy borrows $6,930 from the bank. For a four-year loan, the bank requires annual end-of-year payments of $2,281.86. Calculate the interest rate on the loan.

Herbert has opened a retirement fund account which pays 7 percent interest and requires $5,000 annual deposits. Herbert will retire in 15 years and expects 10 years of retirement life. What is the maximum annual retirement benefit Herbert can get during his retirement years?

You have provided your friend with a service worth $8,500. Your friend offers you the following cash flow instead of paying $8,500 today. Should you accept his offer if your opportunity cost is 8 percent?

The annual percentage yield (APY) is the effective rate of interest that must be disclosed to customers by banks on their savings products as a result of "truth in savings laws."

Mary will receive $12,000 per year for the next 10 years as royalty for her work on a finance book. What is the present value of her royalty income if the opportunity cost is 12 percent?

Congratulations! You have just won the lottery! However, the lottery bureau has just informed you that you can take your winnings in one of two ways. Choice X pays $1,000,000. Choice Y pays $1,750,000 at the end of five years from now. Using a discount rate of 5 percent, based on present values, which would you choose? Using the same discount rate of 5 percent, based on future values, which would you choose? What do your results suggest as a general rule for approaching such problems? (Make your choices based purely on the time value of money.)

The present value of $1,000 received at the end of year 1, $1,200 received at the end of year 2, and $1,300 received at the end of year 3, assuming an opportunity cost of 7 percent, is ________.

Thelma is planning for her son's college education to begin five years from today. She estimates the yearly tuition, books, and living expenses to be $5,000 per year for a four-year degree, assuming th expenses incur only at the end of the year. How much must Thelma deposit today, at an interest rate of 8 percent, for her son to be able to withdraw $5,000 per year for four years of college?

The rate of return earned on an investment of $50,000 today that guarantees an annuity of $10,489 for six years is approximately ________.

Calculate the combined future value at the end of year 3 of $1,000 received at the end of year 1, $3,000 received at the end of year 2, and $5,000 received at the end of year 3, all sums deposited at 5 percent.

Future value is the value of a future amount at the present time, found by applying compound interest over a specified period of time.

Assume you have a choice between two deposit accounts. Account X has an annual percentage rate of 12.25 percent but with interest compounded monthly. Account Y has an annual percentage rate of 12.20 percent with interest compounded continuously. Which account provides the highest effective annual return?

A local brokerage firm is offering a zero-coupon certificate of deposit for $10,000. At maturity, three years from now, the investor will receive $14,000. What is the rate of return on this investment?