Question

Sean receives a portion of his income from his holdings of interest-bearing U.S. government bonds. The bonds offer a real interest rate of 4.5% per year. The nominal interest rate on the bonds adjusts automatically to account for the inflation rate.

The government taxes nominal interest income at a rate of 10%. The following table shows two scenarios: a low-inflation scenario and a high-inflation scenario.

Given the real interest rate of 4.5% per year, find the nominal interest rate on Sean's bonds, the after-tax nominal interest rate, and the after-tax real interest rate under each inflation scenario.

Inflation Rate	Real Interest Rate	Nominal Interest Rate	After-Tax Nominal Interest Rate	After-Tax Real Interest Rate
(Percent)	(Percent)	(Percent)	(Percent)	(Percent)
2.0	4.5
8.5	4.5

Compared with lower inflation rates, a higher 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.

Answer 1

Answer:

Real Interest Rate = Nominal Interest - Inflation Rate

Using this formula we can find Nominal Interest Rate

1. Nominal Interest Rate:

Nominal Interest Rate = Real Interest Rate + Inflation Rate

For First year = 4.5 % + 2.0 %

= 6.50 % will be nominal interest rate for first year

Second year = 4.5 % + 8.5 %

= 13.0 % will be nominal interest rate for second year

2. After-Tax Nominal Interest Rate

After-Tax Nominal Interest Rate = Nominal Interest Rate ( 1 - Tax Rate )

For first year = 6.5 ( 1 - 0.1 )

= 6.5 ( 0.9 )

= 5.85 %

For first year = 13 ( 1 - 0.1 )

= 13 ( 0.9 )

= 11.7 %

3. After-Tax Real Interest Rate

After-Tax Real Interest Rate = Real Interest Rate ( 1 - Tax Rate )

For first year = 4.5 ( 1 - 0.1 )

= 4.5 ( 0.9 )

= 4.05 %

For second year it will be same = 4.05 %

Thus, there is change in nominal interest rate as it includes the effect of inflation rate, but as inflation rises nominal interest rate increase, it will also increases the tax burden on individual.

Thanks