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%

$$\text{After-tax nominal interest rate}=6$$ $$\text{After-tax real interest rate}=5.7$$

Option b:

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

$$\text{After-tax nominal interest rate}=6$$ $$\text{After-tax real interest rate}=4.8$$

Option c:

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

$$\text{After-tax nominal interest rate}=6$$ $$\text{After-tax real interest rate}=4.2$$

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.