Homework (Ch 12) Due Tomorrow at 1 1 PM CST Raphael receives a portion of his in

ID: 1108403 • Letter: H

Question

Homework (Ch 12) Due Tomorrow at 1 1 PM CST Raphael receives a portion of his income from his holdings of interest-bearing US, 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. Given the real interest rate of 45% per year, find the nominal interest rate on Raphaers bonds, the after tax nominal interest rate, and the after-tax Real Interest Rate (Percent) After-Tax Nominal Interest Rate (Percent,) Inflation Rate After-Tax Real (Percent) (Percent) Compared with lower inflation rates, a higher inflation rate wi the quantity of stment in the economy and 2 3 4 6

Explanation / Answer

Answer:-

Inflation Rate

Real interest rate

Nominal interest rate

After tax nominal interest rate

After Tax Real Interest Rate

2.0

4.5

6.5

5.85

3.85

8.5

4.5

11.7

3.2

Reason:-

To maintain the level of the real interest rate, the nominal interest rate must adjust according to the Fisher equation:

Nominal interest rate =Real interest rate + inflation

At the lower inflation rate of 2% per year, the nominal interest rate is 6.5%, the 4.5% real rate plus the 2% inflation rate. At the higher inflation rate of 8.5% per year, the nominal interest rate is 13%, the 4.5% real rate plus the 8.5% inflation rate.

The government taxes 10% of the nominal interest paid on the bonds. When the inflation rate is 2% per year and the nominal interest rate is 6.5% per year, the tax reduces the nominal interest payment from 6.5% to an aftertax nominal interest payment of 6.5%-(0.1*6.5%)=5.85% per year .

At an inflation rate of 8.5% per year and a nominal interest rate of 13% per year, the tax reduces the nominal interest payment from 13% to an aftertax nominal interest payment of 13%-(0.1*13%)=11.7%

Rearranging the nominal interest rate equation, you can see that the real interest rate is the difference between the nominal interest rate and the inflation rate. The aftertax real interest rate is, therefore, the aftertax nominal interest rate minus the inflation rate. At the lower inflation rate, the aftertax real interest rate is calculated as follows:

After tax real interest rate=After tax nominal interest rate – inflation rate

= 5.85%-2% =3.85%

At the higher inflation rate, the aftertax real interest rate is 11.7%-8.5%3.2%, which is lower than the aftertax real return at the lower inflation rate

Answer:- Compared with lower inflation rates, a higher inflation rate will decrease the aftertax real interest rate when the government taxes nominal interest income. This tends to discourage saving, thereby decreasing the quantity of investment in the economy and decreasing the economy's longrun growth rate.

Reason:- When the government taxes nominal interest income, inflation distorts the real returns to saving. Compared with lower rates of inflation, higher inflation rates lead to lower aftertax real interest rates. A lower aftertax real return tends to discourage saving. The economy's level of investment depends on the pool of savings available to finance investment projects like acquiring new tools or machinery or building new plants or office buildings. The lower level of saving will decrease the quantity of investment, thereby decreasing the economy's rate of physical capital accumulation and depressing the longrun economic growth rate. To the extent that the central bank cannot reduce inflation in an economy where government taxes nominal interest income, it will discourage saving, investment, and growth