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 RateReal Interest RateNominal Interest RateAfter-Tax Nominal Interest RateAfter-Tax Real Interest Rate(Percent)(Percent)(Percent)(Percent)(Percent)2.04.5   8.54.5   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.

Question
Asked Nov 20, 2019
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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.

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Expert Answer

Step 1

The nominal interest rate can be calculated using following formula-

Nominal interest rate = Inflation rate + Real interest rate
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Nominal interest rate = Inflation rate + Real interest rate

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Step 2

The table (1) below shows the calculation of required nominal interest rate.

 

Table (1)
Real interest rate (%
Inflation rate (%)
Nominal interest rate
Nominal interest rate
= Inflation rate+ Real
(%)
interest rate
2.0+4.5
8.5+4.5
2.0
4.5
6.5
13
4.5
8.5
co
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Table (1) Real interest rate (% Inflation rate (%) Nominal interest rate Nominal interest rate = Inflation rate+ Real (%) interest rate 2.0+4.5 8.5+4.5 2.0 4.5 6.5 13 4.5 8.5 co

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Step 3

The after-tax nominal interest rate can be ...

After-tax nominal interest rate Nominal interest ratex(1-Tax rate)
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After-tax nominal interest rate Nominal interest ratex(1-Tax rate)

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