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:
The after-tax real interest rate can then be calculated using the formula:
Now let's calculate this for each option:
Option a:
- Nominal interest rate = 6%
- Inflation = 4%
- Tax rate = 5%
Option b:
- Nominal interest rate = 6%
- Inflation = 3%
- Tax rate = 20%
Option c:
- Nominal interest rate = 6%
- Inflation = 2%
- Tax rate = 30%
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.