Answer to Question #202826 in Macroeconomics for SYEDA ZAINAB

Question

Calculating the changes in the after-tax interest rates if the tax rate on interest income changes from 30

Percent to 20 percent. Let the nominal interest rate is 5 percent per year and expected inflation rate is 2

Percent per year.

Answer 1

Solution:

First derive the after-tax interest rates for the previous and new tax rates and find the difference.

Derive the after-tax interest rate of the new tax rate of $20\%$:

After-tax real interest rate = After-tax nominal interest rate – Inflation rate

Derive the tax on nominal interest rate:

Tax rate = $20\%$

Nominal interest rate = $5\%$

$20\%$ tax on nominal interest rate = $0.20\times 5\% = 1\%$

After-tax nominal interest rate = Nominal interest rate – tax on nominal interest rate

After-tax nominal interest rate = $5\% - 1\% = 4\%$

Expected Inflation rate = $2\%$

 

After-tax real interest rate = $4\% - 2\% = 2\%$

Now derive the after-tax interest rate of the new tax rate of $30\%$:

After-tax real interest rate = After-tax nominal interest rate – Inflation rate

Derive the tax on nominal interest rate:

Tax rate = $30\%$

Nominal interest rate = $5\%$

$30\%$ tax on nominal interest rate = $0.30\times 5\% = 1.5\%$

After-tax nominal interest rate = Nominal interest rate – tax on nominal interest rate

After-tax nominal interest rate = $5\% - 1.5\% = 3.5\%$

Expected Inflation rate = $2\%$

 

After-tax real interest rate = $3.5\% - 2\% = 1.5\%$

The change in After-tax real interest rate = $2\% - 1.5\% = 0.5\%$