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# Before- and After-tax Values of One-Time Investment

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A) Someone in the 36 percent tax bracket can earn 9 percent annually on her investment in a tax-exempt IRA account. What will be the value of a one time \$10,000 investment in 5 years? 10 years? 20 years?
b) Suppose the preceding 9 percent is taxable rather then tax-deferred and the taxes are paid annually. What will be the the after-tax value of her \$10,000 investment after 5, 10, 20 years?

#### Solution Preview

a) Someone in the 36 percent tax bracket can earn 9 percent annually on her investment in a tax-exempt IRA account. What will be the value of a one time \$10,000 investment in 5 years? 10 years? 20 years?

There are no taxes to consider, so we can use the basic formula for the future value of \$1, which is:

Future value of \$1=\$1*(1+interest rate)^Number of compounding periods

Thus, in 5 years the \$10,000 will be worth:

Future value of \$10,000=\$10,000*(1.09)^5=\$10,000*1.09*1.09*1.09*1.09*1.09=\$10,000*1.538624=\$15,386.24

In ...

#### Solution Summary

This solution will illustrate how to compute the before- and after-tax values of a one-time investment earning 9 percent after 5, 10 and 20 years,

\$2.19