Question

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Suppose, again, that you put $100 in the bank on January 1, 2017. This time around, however, the annual nominal interest rate is 6 percent and the inflation rate is 4 percent. Much to your chagrin, the federal government treats interest income like wages and salaries and you have to pay income tax. Suppose you are in the 25% income tax bracket.

（1）The real return on your investment, i.e. after you've paid your tax liability is

（2）Now, suppose that the nominal interest rate instead is 12 percent and inflation is 10 percent. In this case, the real return on your $100 deposit is

Answer 1

(1)

Tax is imposed on the nominal interest (return) only.

After-tax nominal interest rate = 6% x (1 - 0.25) = 6% x 0.75 = 4.5%

After-tax real interest rate (return) = After-tax nominal interest rate - Inflation rate = 4.5% - 4% = 0.5%

In dollar terms, After-tax real return = $100 x 0.5% = $0.50

(2)

After-tax nominal interest rate = 12% x (1 - 0.25) = 12% x 0.75 = 9%

After-tax real interest rate (return) = After-tax nominal interest rate - Inflation rate = 9% - 10% = - 1%

In dollar terms, After-tax real return = $100 x (- 1%) = -$1