Chapter 4, Problem 4.1C

If you invest $500 for one year at a rate of 8 percent per year, how much interest will you earn?

Summary Introduction

To calculate: The interest earned.

Introduction:

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

Answer to Problem 4.1C

The interest earned on $500 is $40.

Explanation of Solution

Given information:

Person X invests $500 for one year. The rate of interest is 8 percent.

The formula to calculate the future value:

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

Where,

“FV” refers to the future value or the current market value

“PV” refers to the present value

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

Compute the future value of investment:

$\begin{array}{c}\text{FV}=\text{PV}\times {\left(1+r\right)}^t\\ =\$500\times {\left(1+0.08\right)}^1\\ =\$500\times 1.08\\ =\$540\end{array}$

Hence, the value of deposit after one year is $540.

Compute the interest earned:

The difference between the future value and the present value is the interest earned on the investment. The deposit value is $500. After one year, Person X receives $540. Hence, the interest received on the deposit is $40$(\$540-\$500)$.