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