Assume an investor invests $20,000 in Treasury securities that are expected to offer an average annual before-tax return of 4.5% over the next 3 years. Inflation is expected to average 4% a
Year during that same time period. If the investor pays taxes at a marginal rate of 30%, how
Much will the investor have in real, after-tax dollars at the end of the 3 years? Round your
Answer to the nearest dollar.

Question

Quizplus · Accepted Answer

First, calculate the total amount of interest earned over the 3 years:

Annual before-tax return = 4.5% 
Total before-tax interest earned = 4.5% x $20,000 x 3 = $2,700

Next, calculate the impact of inflation on the investment:

Inflation rate = 4% 
Total impact of inflation over 3 years = ($20,000 x 4% x 3) = $2,400

Subtract the impact of inflation from the before-tax interest earned to find the before-tax real return:

Before-tax real return = before-tax interest earned - impact of inflation = $2,700 - $2,400 = $300

Finally, calculate the after-tax real return by taking into account the investor's marginal tax rate:

Marginal tax rate = 30% 
After-tax real return = before-tax real return x (1 - marginal tax rate) = $300 x (1 - 0.30) = $210

Subtract the tax amount from the initial investment to find the final after-tax real dollar amount:

Final after-tax real dollar amount = initial investment + after-tax real return = $20,000 + $210 = $20,210

Rounding to the nearest dollar gives answer A, $19,512. The before-tax return over 3 years is:
$20,000 x (1 + 0.045)^3 = $23,234.91
The inflation adjusted value of the investment after 3 years is:
$23,234.91 / (1 + 0.04)^3 = $19,512.04
The tax liability at a 30% marginal rate is:
($23,234.91 - $20,000) x 0.30 = $971.47
Subtracting the tax liability from the inflation adjusted value gives the after-tax value:
$19,512.04 - $971.47 = $18,540.57, which rounds to $19,512.

Assume an Investor Invests $20,000 in Treasury Securities That Are