Carlos receives a portion of his income from his holdings of interest-bearing U.
ID: 1201131 • Letter: C
Question
Carlos 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 Carlos's bonds, the after-tax nominal interest rate, and the after-tax real interest rate under each inflation scenario. 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.Explanation / Answer
Nominal interest rate = Real interest rate + Inflation rate
After-tax nominal interest rate = Nominal interest rate * ( 1 - tax rate)
After-tax real interest rate = After-tax nominal interest rate - Inflation rate
Tax rate = 10% or 0.10
Following is the complete table -
Real interest rate
Nominal interest rate
After-tax nominal interest rate
As above table shows that compared with lower inflation rates, a higher inflation rate will decrease the after-tax real interest rate when government taxes nominal interest income.
This fall in after-tax real interest rate will adversely impact the savings that is this tends to decrease saving, thereby reducing the quantity of investment in the economy and lowering or decreasing the economy's long-run growth rate.
Inflation rateReal interest rate
Nominal interest rate
After-tax nominal interest rate
After-tax real interest rate 2.0 4.5 2.0 + 4.5 = 6.5 6.5*(1 - 0.10) = 5.85 5.85 - 2.0 = 3.85 9.5 4.5 9.5 + 4.5 = 14 14*(1 - 0.10) = 12.6 12.6 - 9.5 = 3.1