Question

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.

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**.