Chapter 24, Problem 7MCQ

To determine

The correct option that determines the situation occurs due to the increase in interest rate.

Answer to Problem 7MCQ

Option a is correct.

Explanation of Solution

Explanation for the correct option:

a.

If the interest rate is increased, then it means that amount of $1 borrowed at 10% will be borrowed at 11% or higher. If this happens, then the present value of the asset will decrease. This is calculated by using the PV formula which is as follows:

  $\text{PV}=\text{FV}\left(\frac{1}{{\left(1+r\right)}^n}\right)$

For instance, if the interest rate is increased to 20% which was 10% earlier, then the price of the bond with face value changes to $833.33 from $909.091 if its present value is $1000 which is calculated as follows:

  $\begin{array}{c}{\text{PV}}_{10\%}=\$1000\left(\frac{1}{{\left(1+.10\right)}^1}\right)\\ =\$1000\times 0.90909\\ =\$909.091\\ {\text{PV}}_{20\%}=\$1000\left(\frac{1}{{\left(1+.20\right)}^1}\right)\\ =\$1000\times 0.83333\end{array}$

The prices of the bond will decrease as the interest rate increases. Therefore, option a is correct.

Explanation for incorrect options:

b.

If the interest rate increases then the future value also increases but the present value decreases. Therefore, option b is incorrect.

c.

Net present value decreases with the increase in interest rate as there is an inverse relationship between the two. Therefore, option c is incorrect.

d.

If the interest rate or the discount rate of a project is increased then the cost of borrowing also increases. Therefore, option d is incorrect.

e.

The opportunity cost refers to the cost of spending on other alternatives. This cost increases as the interest rate increases which increases the borrowing rates. Therefore, option e is incorrect.

Economics Concept Introduction

Interest rates: The rates that were charged by the investor who is ready to lend his/her money for a certain period of time to the borrower.

Present value of money: This is the concept that is used by every investor or financial dealer where the value of the dollar received today is compared with the value of the dollar that is expected to be received later by using interest rates.