Chapter 24, Problem 2MCQ

To determine

The correct option that determines the present value of the amount if the interest rate is zero.

Answer to Problem 2MCQ

Option b is correct.

Explanation of Solution

Explanation for the correct option:

b.

The present value of the dollar can be determined by using the following formula:

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

If interest becomes zero, then the present value and future value will be the same as there is no effect of discounting. Therefore, option b is correct.

Explanation for incorrect options:

a.

If the interest rate is more than zero, then the present value will be less than $1. Therefore, option a is correct.

c.

Future value should be higher than the present value as the dollar amount received today is of greater value than the same amount received after a year. Therefore, option c is incorrect.

d.

If the value of r is zero then PV will be equal to FV as per the formula mentioned. It can be calculated as follows:

  $\begin{array}{c}\text{PV=FV}\left(\frac{\text{1}}{{\left(\text{1+0}\right)}^{\text{n}}}\right)\\ \text{PV=FV}\left(\text{1}\right)\end{array}$

Therefore, option d is incorrect.

e.

If the interest rate is zero, then the present value will be equal to the future value. 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.