Steve receives a portion of his income from his holdings of interest-bearing U.S

Question

Steve receives a portion of his income from his holdings of interest-bearing U.S. government bonds. The bonds offer a real interest rate of 3.5% per year. The nominal interest rate on the bonds adjusts automatically to the inflation rate. Suppose the government taxes nominal interest income at a rate of 20%. The following table shows two scenarios, a low-inflation scenario and a high-inflation scenario. Given the real interest rate of 3.5% per year, find the nominal interest rate on Steve's bonds, the after-tax nominal interest rate, and the after-tax real interest rate under each inflation scenario. Compared with higher inflation rates, a lower inflation rate will_____the after-tax real interest rate when the government taxes nominal interest income. This tends to____saving, thereby___the quantity of investment in the economy and____the economy's long-run growth rate.

Explanation / Answer

The equation of exchange is given as :

Real interest = nominal interest - inflation.

Also, the after tax nominal interest rate = nominal interest* (1 - T)

where T = tax = 20% or 0.20

After tax real interest = after tax nominal interest - inflation.

For lower inflation :

3.5% = nominal interest - 2.5%

Nominal interest = 6%

After tax nominal = 6% * (1 - 0.20

After tax nominal = 6% * 0.80

After tax nominal = 4.8%

After tax real = 4.8 - 2.5

After tax real = 2.3%

For higher inflation :

3.5% = nominal interest - 6.5%

Nominal interest = 10%

After tax nominal = 10% * 0.80

After tax nominal = 8%

After tax real = 8 - 6.5

After tax real = 1.5%.

Increases. The lower inflation would increase the real interest rates.

Higher.

Increasing

Increasing.

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