Nick receives a profit of his income from his holdings of interest-bearing U.S.

Question

Nick receives a profit of his income from his holdings of interest-bearing U.S. government bonds. The bonds offer a real interest rate of 4% per year. The normal interest rate on the bonds adjusts automatically to account for the inflation rate. 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 4% per year, find the nominal interest rate on Nick's bonds, the after-tax nominal interest rate, and the after-tax real interest rate under each inflation scenario. Compared with higher rates, a lower inflation rate will the after-tax real interest rate when the government taxes nominal interest income. This tens to saving, thereby the quantity of investment in the economy and the economy's long-run growth rate.

Explanation / Answer

Nominal interest rate is the rate that you receive i.e if you receive $ 105 after a year for an investment of $ 100, the nominal interest rate is 5 %.

Real interest rate is the actual rate of interest i.e nominal interest rate adjusted for inflation .i.e.: real interest rate = nominal interest rate - inflation

After tax nominal rate = nominal rate - tax, in this case = nominal rate - 0.2 nominal rate = 0.8 nominal rate

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

So, using above computation, for inflation rate of 1.5 & real interest rate of 4

nominal interest rate = 4 + 1.5 = 5.5 %

after tax nominal interest rate = 0.8 * 5.5 = 4.4 %

after tax real interest rate = 4.4 - 1.5 = 2.9 %

for inflation rate of 8 & real interest rate of 4

nominal interest rate = 4 + 8 = 12 %

after tax nominal interest rate = 0.8 * 12 = 9.6 %

after tax real interest rate = 9.6 - 8 = 1.6 %

Hence,

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

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