Chapter 24, Problem 2FRQ

a.

To determine

The future value of a three-year loan of $1000 be 5%.

Explanation of Solution

Given information:

Present value is $1000

Number of years is 3

Interest rate is 5%

Calculations:

Future value by using $PV x (1+interest rate)^number of years can be computed which is as follows:

  $\begin{array}{c}\text{FV=PV}{\left(\text{1+r}\right)}^{\text{n}}\\ \text{=\$1000}{\left(\text{1}\text{.05}\right)}^{\text{3}}\\ \text{=\$1000}\left(\text{1}\text{.15763}\right)\\ \text{=\$1157}\text{.63}\end{array}$

Economics Concept Introduction

Future value: Future value of $1 will be determined by using $1($1+r) which means the future value of $1 will be greater due to the growth rate.

b.

To determine

The present value of $1000 received in 3 years at a 5% interest rate.

Explanation of Solution

Given information:

Present value is $1000

Number of years is 3

Interest rate is 5%

Calculations:

Future value by using $FV x 1/(1+interest rate)^number of years can be computed which is as follows:

  $\begin{array}{c}\text{PV=FV×}\frac{\text{1}}{{\left(\text{1+r}\right)}^{\text{n}}}\\ \text{=\$1000×}\frac{\text{1}}{{\left(\text{1}\text{.05}\right)}^{\text{3}}}\\ \text{=\$1000×}\frac{\text{1}}{\left(\text{1}\text{.15763}\right)}\\ \text{=\$863}\text{.838}\end{array}$

Economics Concept Introduction

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.