Question

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?

Answer 1

a) value of investment in 5 years $=10000\times (1+0.09)^{5}=\$15386.2$

value of investment in 10 years$=10000\times (1+0.09)^{10}=\$23673.6$

value of in vestment in 20 years$=10000\times (1+0.09)^{20}=\$56044.1$

if taxes are applied, the rate will become $0.09(1-0.35)=0.0585=5.85\%$

b) value of investment in 5 years $=10000\times(1+0.0585)^{5}=\$13287.8$

value of investment in 10 years$=10000\times (1+0.0585)^{10}=\$17656.7$

value of investment in 20 years$=10000\times (1+0.0585)^{20}=\$31175.8$