Chapter 30, Problem 6PA

Subpart (a):

To determine

Real interest rate before and after the tax.

Explanation of Solution

Before the tax real interest rate is calculated using the formula:

${\text{Real interest rate}}_{\text{Before tax}}={\text{Nominal interest rate}}_{\text{Before tax}}-\text{inflation rate}$ (1)

Substitute the respective values in equation (1) to calculate the real interest rate.

$\begin{array}{c}{\text{Real interest rate}}_{\text{Before tax}}=\text{10}-\text{5}\\ =\text{5}\end{array}$

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:

$\begin{array}{c}\text{Reduction in NI = }\frac{40}{100}\times \text{ Nominal interest rate}\\ \text{= 0}\text{.4}\times \text{10}\\ \text{= 4}\end{array}$

Thus, reduction in nominal interest rate due to tax is 4%.

After the tax nominal interest rate is calculated using the formula:

${\text{Nominal interest rate}}_{\text{After tax}}=\left(\begin{array}{l}{\text{Nominal interest}}_{\text{Before tax}}\\ -\text{Reduction in normal interest}\end{array}\right)$ (2)

Substitute the respective values in equation (2) to calculate the nominal interest rate.

$\begin{array}{c}{\text{Nominal interest rate}}_{\text{After tax}}=\text{10}-\text{4}\\ =\text{6}\end{array}$

Thus, after the tax nominal interest rate is 6%.

After the tax real interest rate is calculated using the formula:

${\text{Real interest rate}}_{\text{After tax}}={\text{Nominal interest rate}}_{\text{After tax}}-\text{inflation rate}$ (3)

Substitute the respective values in equation (3) to calculate the real interest rate.

$\begin{array}{c}{\text{Real interest rate}}_{\text{After tax}}=\text{6}-\text{5}\\ =\text{1}\end{array}$

Thus, after the tax real interest rate is 1%.

Economics Concept Introduction

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):

To determine

Real interest rate before and after the tax.

Explanation of Solution

Substitute the respective values in equation (1) to calculate real interest rate before tax.

$\begin{array}{c}{\text{Real interest rate}}_{\text{Before tax}}=\text{6}-\text{2}\\ =\text{4}\end{array}$

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:

$\begin{array}{c}\text{Reduction in NI = }\frac{40}{100}\times \text{ Nominal interest rate}\\ \text{= 0}\text{.4}\times 6\\ \text{= 2}\text{.4}\end{array}$

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.

$\begin{array}{c}{\text{Nominal interest rate}}_{\text{After tax}}=\text{6}-\text{2}\text{.4}\\ =\text{3}\text{.6}\end{array}$

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.

$\begin{array}{c}{\text{Real interest rate}}_{\text{After tax}}=\text{3}\text{.6}-\text{2}\\ =1.6\end{array}$

Thus, after the tax real interest rate is 1.6%.

Economics Concept Introduction

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):

To determine

Real interest rate before and after the tax.

Explanation of Solution

Substitute the respective values in equation (1) to calculate the real interest rate before tax.

$\begin{array}{c}{\text{Real interest rate}}_{\text{Before tax}}=\text{4}-\text{1}\\ =\text{3}\end{array}$

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:

$\begin{array}{c}\text{Reduction in NI = }\frac{40}{100}\times \text{ Nominal interest rate}\\ \text{= 0}\text{.4}\times 4\\ \text{= 1}\text{.6}\end{array}$

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.

$\begin{array}{c}{\text{Nominal interest rate}}_{\text{After tax}}=\text{4}-\text{1}\text{.6}\\ =\text{2}\text{.4}\end{array}$

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.

$\begin{array}{c}{\text{Real interest rate}}_{\text{After tax}}=\text{2}\text{.4}-\text{1}\\ =\text{1}\text{.4}\end{array}$

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.

Economics Concept Introduction

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.