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. \[ \text{Nominal Interest Rate} = \text{Real Interest Rate} + \text{Inflation Rate} = 4% + 2% = 6% \]

   Now, we'll calculate the after-tax nominal interest rate: \[ \text{After-tax Nominal Interest Rate} = \text{Nominal Interest Rate} \times (1 - \text{Tax Rate}) \] \[ = 6% \times (1 - 0.25) = 6% \times 0.75 = 4.5% \]

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.