Given a nominal interest rate of 6 percent, in which of the following cases would you earn the lowest after-tax real rate of interest?

a.

Inflation is 4 percent; the tax rate is 5 percent.
b.

Inflation is 3 percent; the tax rate is 20 percent.
c.

Inflation is 2 percent; the tax rate is 30 percent.
d.

The after-tax real interest rate is the same for all of the above.

1 answer

To determine which option provides the lowest after-tax real rate of interest, we first need to calculate the after-tax nominal interest rate and then adjust for inflation.

The formula to calculate the after-tax nominal interest rate is:

After-tax nominal interest rate=Nominal interest rate×(1Tax rate)

The after-tax real interest rate can then be calculated using the formula:

After-tax real interest rate=After-tax nominal interest rateInflation rate

Now let's calculate this for each option:

Option a:

  • Nominal interest rate = 6%
  • Inflation = 4%
  • Tax rate = 5%

After-tax nominal interest rate=6 After-tax real interest rate=5.7

Option b:

  • Nominal interest rate = 6%
  • Inflation = 3%
  • Tax rate = 20%

After-tax nominal interest rate=6 After-tax real interest rate=4.8

Option c:

  • Nominal interest rate = 6%
  • Inflation = 2%
  • Tax rate = 30%

After-tax nominal interest rate=6 After-tax real interest rate=4.2

Summary of After-tax Real Interest Rates:

  • Option a: 1.7%
  • Option b: 1.8%
  • Option c: 2.2%

The lowest after-tax real rate of interest is in Option a (1.7%). Therefore, the answer is Option a.