Appendix II: Compound Interest and the Concept of Present Value

What is meant by the term compound interest?

Explain in words the following future-value formula: F n = P (1 + r ) n.

Define the term present value.

"The greater the discount rate, the greater the present value of a future cash flow." True or false? Explain your answer.

"If the interest rate is 10 percent, a present value of $100 and a future value of $161.10 at the end of five years are economically equivalent. " Explain.

What is an annuity?

Answer each of the following independent questions. Ignore personal income taxes. 1. Suppose you invest $2,500 in an account bearing interest at the rate of 14 percent per year. What will be the future value of your investment in six years? 2. Your best friend won the state lottery and has offered to give you $10,000 in five years, after he has made his first million dollars. You figure that if you had the money today, you could invest it at 12 percent annual interest. What is the present value of your friend's future gift? 3. In four years, you would like to buy a small cabin in the mountains. You estimate that the property will cost you $52,500 when you are ready to buy. How much money would you need to invest each year in an account bearing interest at the rate of 6 percent per year in order to accumulate the $52,500 purchase price? 4. You have estimated that your educational expenses over the next three years will be $13,000 per year. How much money do you need in your account now in order to withdraw the required amount each year? Your account bears interest at 10 percent per year.

Refer to the answers given for the preceding exercise. Required: 1. Refer to requirement (1) of the preceding exercise. Prepare a display similar to Exhibit II-1 to show how your accumulation grows each year to equal $5,487.50 after six years. 2. Refer to requirement (4) of the preceding exercise. Prepare a display similar to Exhibit II-3 to verify that $32,331 is the amount you need to fund your educational expenses.

You plan to retire at age 40 after a highly successful but short career. You would like to accumulate enough money by age 40 to withdraw $225,000 per year for 40 years. You plan to pay into your account 15 equal installments beginning when you are 25 and ending when you are 39. Your account bears interest of 12 percent per year. Required: 1. How much do you need to accumulate in your account by the time you retire? 2. How much do you need to pay into your account in each of the 15 equal installments? 3. Is this a future-value problem or a present-value problem? Explain.