Chapter 3.6, Problem 1E

Solution

To find: The amount $A$ accumulated after investing a principal $P$ for $t$ years at an interest rate $r$ compounded annually and for simple interest at the same rate $r$ .

The amount is $\$2,251.10$ .

The simple interest is $\$2,130$ .

Given information:

It is given that $P=\$1500,r=7\%,t=6$ .

Concept Used:

Interest Computed Using Simple Interest If a principal $P$ is invested at a fixed annual interest rate $r$ , calculated at the end of each year, then the value of the investment after $n$ years is $A=P\left(1+rn\right)$ where $r$ is expressed as a decimal.

Interest Computed Using Compound Interest

If a principal $P$ is invested at a fixed annual interest rate $r$ , calculated at the end of each year, then the value of the investment after $n$ years is $A=P{\left(1+r\right)}^n$ where $r$ is expressed as a decimal.

Calculation:

Here, $P=\$1500,r=0.07,t=6$

Interest Computed Using Simple Interest

Substitute $P$ for $\$1500$ , $r$ for $0.07$ , and $t$ for $6$ , in $A=P\left(1+rn\right)$ .

  $\begin{array}{c}A=1500\left(1+\left(0.07\cdot 6\right)\right)\\ =1500\left(1.42\right)\\ =\$2,130\end{array}$

Interest Computed Using Compound Interest

Substitute $P$ for $\$1500$ , $r$ for $0.07$ , and $t$ for $6$ , in $A=P{\left(1+r\right)}^n$ .

  $\begin{array}{c}A=1500{\left(1+0.07\right)}^6\\ =1500{\left(1.07\right)}^6\\ =\$2,251.10\end{array}$

Hence, the interest Computed Using Simple Interest is $\$2,130$ and interest Computed Using Compound Interest is $\$2,251.10$ .