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# Questions about Present and Future Value

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1. Future Value
If you invest \$9,000 today, how much will you have:
a. In 2 years at 9 percent?
b. In 7 years at 12 percent?
c. In 25 years at 14 percent?
d. In 25 years at 14 percent (compounded semiannually)

2. Present Value
How much would you have to invest today to receive:
a. \$15,000 in 8 years at 10 percent?
b. \$20,000 in 12 years at 12 percent?
c. \$6,000 each year for 10 years at 9 percent?
d. \$50,000 each year for 50 years at 7 percent?

3. Future Value
If you invest \$2,000 a year in a retirement account, how much will you have:
a. In 5 years at 6 percent?
b. In 20 years at 10 percent?
c. In 40 years at 12 percent?

4. Present Value
Jack Hammer invests in a stock that will pay dividends of \$2.00 at the end of the first year: \$2.20 at the end of the second year; and \$2.40 at the end of the third year. Also, he believes that at the end of the third year he will be able to sell the stock for \$33. What is the present value of all future benefits if a discount rate of 11 percent is applied? (Round all values to two places to the right of the decimal point.)

#### Solution Preview

1. Future Value

To find the future value we use the compound interest formula
FV = PV X (1+r)^n
Where PV = present value
r = rate of interest
n = time period

If you invest \$9,000 today, how much will you have:
a. In 2 years at 9 percent?

FV = 9,000 X (1.09)^2 = \$10,692.9

b. In 7 years at 12 percent?

FV = 9,000 X (1.12)^7 = \$19,896.13

c. In 25 years at 14 percent?

FV = 9,000 X (1.14)^25 = \$238,157.24

d. In 25 years at 14 percent (compounded semiannually)

When the compounding is not annual, the rate = r/a and time period is n*a where a is the compounding frequency. Here the compounding frequency is 2 for semi-annual (twice a year)
Rate = 14%/2=7%
Time period = 25X2=50
FV = 9,000 X (1.07)^50 = \$265,113.23

2. Present ...

#### Solution Summary

The solution explains how to calculate the present value and future value in a variety of circumstances.

\$2.19