Chapter 4, Problem 1P

Compare the interest earned by $9,000 for five years at 8% simple interest with interest earned by the same amount for five years at 8% compounded annually. Explain why a difference occurs. (4.2)

To determine

Reason for different interest amount.

Explanation of Solution

Time period is denoted by n. Interest rate is denoted by i. Simple interest can be calculated as follows.

$\begin{array}{c}\text{Simple interest}=\text{Principle}\times \text{Interest rate}\times \text{n}\\ =9,000\times 0.08\times 5\\ =3,600\end{array}$

Simple interest is 3,600.

Compound interest can be calculated as follows.

$\begin{array}{c}\text{Compound interest}=\text{Principle}{\left(1+\text{i}\right)}^{\text{n}}-\text{Principle}\\ =9,000{\left(1+\text{i}\right)}^{\text{5}}-9,000\\ =9,000\left(1.4693\right)-9,000\\ =4,223.7\end{array}$

Compound interest is $4,223.7. The compound interest is greater by $823.7 than the simple interest. The reason for greater interest for the compounding interest rate is that the previous interest payment added to the principal for the next year interest payment. But, simple interest payment calculate the interest only for the principal payment.