# Investments

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Submitted By jtwhitley
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Chapter 2 Homework:

4. a. Someone in the 36 percent tax bracket can earn 9 percent annually on her investments 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 return is taxable rather than tax-deferred and the taxes are paid annually. What will be the after-tax value of her \$10,000 investment after 5, 10, and 20 years?

5. a. Someone in the 15 percent tax bracket can earn 10 percent on his investments in a tax exempt IRA account. What will be the value of a \$10,000 investment in 5 years? 10 years? 20 years?

b. Suppose the preceding 10 percent return is taxable rather than tax-deferred. What will be the after-tax value of his \$10,000 investment after 5, 10, and 20 years?

6. Assume that the rate of inflation during all these periods was 3 percent a year. Compute the real value of the two tax-deferred portfolios in problems 4a and 5a.

Solution:

a. \$10,000 invested in 9 percent tax-exempt IRA (assuming annual compounding)

In 5 years: \$10,000(FVIF @ 9%) = \$10,000(1.5386) = \$15,386

In 10 years: \$10,000(FVIF @ 9%) = \$10,000(2.3674) = \$23,674in 20 years

In 20 years: \$10,000(FVIF @ 9%) = \$10,000(5.6044) = \$56,044

(b).

After-tax yield = Before-tax yield (1 - Tax rate)

= 9% (1 - .36)

= 5.76%

\$10,000 invested at 5.76 percent (assuming annual compounding)

in 5 years: \$10,000(FVIF @ 5.76%) = \$13,231

in 10 years: \$10,000(FVIF @ 5.76%) = \$17,507

in 20 years: \$10,000(FVIF @ 5.76%) = \$30,650

Solution 5:

(a). \$10,000 invested in 10 percent tax-exempt IRA (assuming annual compounding)

In 5 years: \$10,000(FVIF @ 10%) = \$25,937

In 20 years: \$10,000(FVIF @ 10%) = \$10,000(6.7275) = \$67,275

(b). After-tax yield = Before-tax yield (1 - Tax rate)

= 10% (1 - .15)

=

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