Question

Lorenzo 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% 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 3% per year, find the nominal interest rate on Lorenzo'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) 2.5 3.0 6.5 3.0 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.

Answer 1

Inflation rate(%)	Real interest rate(%)	Nominal real Interest(%)	After-tax nominal interest rate(%)	After-tax real interest rate(%)
2.5	3.0	5.5	4.95	2.45
6.5	3.0	9.5	8.55	2.05

Compared with higher inflation rates, a lower inflation rate will decreases the after-tax real interest rate when the government taxes nominal interest income. This tends to decrease saving, thereby decrease the quantity of investment in the economy and lower the economy's long-run growth rate.

Nominal interest rate = real interest rate + inflation rate

After tax Nominal interest rate = Nominal interest rate(1-tax rate)

After tax real interest rate = real interest rate * (1-tax rate) - inflation rate * tax rate