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 yields the lowest after-tax real rate of interest, we need to calculate the after-tax nominal interest rate and then adjust for inflation for each case.

1. **Calculate After-Tax Nominal Interest Rate**:
\[
\text{After-Tax Nominal} = \text{Nominal Rate} \times (1 - \text{Tax Rate})
\]

2. **Calculate After-Tax Real Interest Rate**:
\[
\text{After-Tax Real} = \text{After-Tax Nominal} - \text{Inflation Rate}
\]

Let's perform these calculations for each case:

### Case (a):
- Nominal Interest Rate: 6%
- Inflation: 4%
- Tax Rate: 5%

\[
\text{After-Tax Nominal} = 6\% \times (1 - 0.05) = 6\% \times 0.95 = 5.7\%
\]
\[
\text{After-Tax Real} = 5.7\% - 4\% = 1.7\%
\]

### Case (b):
- Nominal Interest Rate: 6%
- Inflation: 3%
- Tax Rate: 20%

\[
\text{After-Tax Nominal} = 6\% \times (1 - 0.20) = 6\% \times 0.80 = 4.8\%
\]
\[
\text{After-Tax Real} = 4.8\% - 3\% = 1.8\%
\]

### Case (c):
- Nominal Interest Rate: 6%
- Inflation: 2%
- Tax Rate: 30%

\[
\text{After-Tax Nominal} = 6\% \times (1 - 0.30) = 6\% \times 0.70 = 4.2\%
\]
\[
\text{After-Tax Real} = 4.2\% - 2\% = 2.2\%
\]

### Summary of Results:
- Case (a): After-Tax Real = 1.7%
- Case (b): After-Tax Real = 1.8%
- Case (c): After-Tax Real = 2.2%

### Conclusion:
Case (a), with an After-Tax Real Interest Rate of 1.7%, earns the lowest after-tax real rate of interest.

Thus, the answer is **(a)**.