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# Various Investment-Based Problems

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1. A saver places \$1,000 in a certificate of deposit that matures after 20 years and that each year pays 4 percent interest, which is compounded annually until the certificate matures.
a) How much interest will the saver earn if the interest is left to accumulate?
b) How much interest will the saver earn if the interest is withdrawn each year?
c) Why are the answers to (a) and (b) different?

2. At the end of each year a self-employed person deposits \$1,500 in a retirement account that earns 10 percent annually.
a) How much will be in the account when the individual retires at the age of 65 if the contributions start when the person is 45 years old?
b) How much additional money will be in the account if the individual stops making the contribution at the age 65 but defers retirement until age 70?
c) How much additional money will be in the account if the individual continues making the contribution but defers retirement until age 70?
d) Compare the answers to (b) and (c). What is the effect of continuing the contributions? How much is the difference between the two answers?

3. Graduating seniors may earn \$45,000 each year. If the annual rate of inflation is 2 percent, what must these graduates earn after 20 years to maintain their current purchasing power? If the rate of inflation rises to 4 percent, will they be maintaining their standard of living if they earn \$100,000 after 20 years?

4. You are offered \$900 five years from now or \$150 at the end of each year for the next five years. If you can earn 6 percent on your funds, which offer will you accept? If you can earn 14 percent on your funds, which offer will you accept? Why are your answers different?

#### Solution Preview

1.
a) How much interest will the saver earn if the interest is left to accumulate?
Present Value of deposit=PV=\$1000
Number of periods=n=20
Rate of interest=r=4%
Future Value of deposit=FV=PV*(1+r)^n=1000*(1+4%)^20=\$2191.12
Interest earned=FV-PV=2191.12-1000=\$1191.12

b) How much interest will the saver earn if the interest is withdrawn each year?
Interest earned per year=PV*r=1000*4%=\$40
Interest earned in 20 years=40*20=\$800

c) Why are the answers to (a) and (b) different?
It is because of the fact that interest is reinvested every year and is added to principal amount in the first case. So, earnings are more.

2.

a) How much will be in the account when the ...

#### Solution Summary

There are four investment based problems. Solutions to these problems depict the methodology to calculate present and future values.

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