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?

Question

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.

Answer 1

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:

\[ \text{After-tax nominal interest rate} = \text{Nominal interest rate} \times (1 - \text{Tax rate}) \]

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

\[ \text{After-tax real interest rate} = \text{After-tax nominal interest rate} - \text{Inflation rate} \]

Now let's calculate this for each option:

Option a:

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

\[ \text{After-tax nominal interest rate} = 6% \times (1 - 0.05) = 6% \times 0.95 = 5.7% \] \[ \text{After-tax real interest rate} = 5.7% - 4% = 1.7% \]

Option b:

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

\[ \text{After-tax nominal interest rate} = 6% \times (1 - 0.20) = 6% \times 0.80 = 4.8% \] \[ \text{After-tax real interest rate} = 4.8% - 3% = 1.8% \]

Option c:

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

\[ \text{After-tax nominal interest rate} = 6% \times (1 - 0.30) = 6% \times 0.70 = 4.2% \] \[ \text{After-tax real interest rate} = 4.2% - 2% = 2.2% \]

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.