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 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).