You put money into an account and earn a real interest rate of 4 percent. Inflation is 2 percent, and your marginal tax rate is 25 percent. What is your after-tax real rate of interest?

Question

a. 1.5 percent
b. 4.5 percent
c. 2.5 percent
d. 5.0 percent

Answer 1

To calculate the after-tax real rate of interest, we first need to determine the after-tax nominal interest rate, and then adjust it for inflation to get the after-tax real rate.

1. Calculate the after-tax nominal interest rate: The nominal interest rate (before tax) is given as the real interest rate plus the inflation rate. $$\text{Nominal Interest Rate}=\text{Real Interest Rate}+\text{Inflation Rate}=4$$

   Now, we'll calculate the after-tax nominal interest rate: $$\text{After-tax Nominal Interest Rate}=\text{Nominal Interest Rate}\times (1-\text{Tax Rate})$$ $$=6$$

2. Calculate the after-tax real interest rate: To find the after-tax real interest rate, we use the formula: $$1+\text{Nominal Rate}=(1+\text{Real Rate})(1+\text{Inflation Rate})$$ Rearranging, we can solve for the after-tax real rate: $$1+\text{After-tax Real Rate}=\frac{1+\text{After-tax Nominal Rate}}{1+\text{Inflation Rate}}$$ Plugging in our values: $$1+\text{After-tax Real Rate}=\frac{1+0.045}{1+0.02}=\frac{1.045}{1.02}\approx 1.0245$$

   Therefore, we find: $$\text{After-tax Real Rate}\approx 1.0245-1=0.0245\text{ or }2.45$$

The closest answer to 2.45% is c. 2.5 percent.