Subpart (a):
Real interest rate before and after the tax.
Subpart (a):
Explanation of Solution
Before the tax real interest rate is calculated using the formula:
Substitute the respective values in equation (1) to calculate the real interest rate.
Thus, before the tax real interest rate is 5%.
The reduction in the nominal interest rate (Reduction NI) due to 40% tax is given as follows:
Thus, reduction in nominal interest rate due to tax is 4%.
After the tax nominal interest rate is calculated using the formula:
Substitute the respective values in equation (2) to calculate the nominal interest rate.
Thus, after the tax nominal interest rate is 6%.
After the tax real interest rate is calculated using the formula:
Substitute the respective values in equation (3) to calculate the real interest rate.
Thus, after the tax real interest rate is 1%.
Concept introduction:
Inflation: It is an increase in the general price level of goods and services in an economy over a period.
Nominal interest rate: It is the interest rate that measures the change in dollar amounts.
Real interest rate: It is the interest rate adjusted with inflation, which is measured by the difference between nominal interest rate and inflation rate.
Subpart (b):
Real interest rate before and after the tax.
Subpart (b):
Explanation of Solution
Substitute the respective values in equation (1) to calculate real interest rate before tax.
Thus, before the tax real interest rate is 4%.
The reduction in the nominal interest rate (Reduction NI) due to 40% tax is given as follows:
Thus, reduction in nominal interest rate due to tax is 2.4%.
Substitute the respective values in equation (2) to calculate the nominal interest rate after tax.
Thus, after the tax nominal interest rate is 3.6%.
Substitute the respective values in equation (3) to calculate the real interest rate after tax.
Thus, after the tax real interest rate is 1.6%.
Concept introduction:
Inflation: It is an increase in the general price level of goods and services in an economy over a period.
Nominal interest rate: It is the interest rate that measures the change in dollar amounts.
Real interest rate: It is the interest rate adjusted with inflation, which is measured by the difference between nominal interest rate and inflation rate.
Subpart (c):
Real interest rate before and after the tax.
Subpart (c):
Explanation of Solution
Substitute the respective values in equation (1) to calculate the real interest rate before tax.
Thus, before the tax real interest rate is 3%.
The reduction in the nominal interest rate (Reduction NI) due to 40% tax is given as follows:
Thus, reduction in nominal interest rate due to tax is 1.6%.
Substitute the respective values in equation (2) to calculate the nominal interest rate after tax.
Thus, after the tax nominal interest rate is 2.4%.
Substitute the respective values in equation (3) to calculate the real interest rate after tax.
Thus, after the tax real interest rate is 1.4%.
From the results, it can be inferred that the after-tax real interest rate is much lower than the before-tax real interest rate.
Concept introduction:
Inflation: It is an increase in the general price level of goods and services in an economy over a period.
Nominal interest rate: It is the interest rate that measures the change in dollar amounts.
Real interest rate: It is the interest rate adjusted with inflation, which is measured by the difference between nominal interest rate and inflation rate.
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