Chapter 6.6, Problem 30IP

To determine

To find: Simple interest rate.

Answer to Problem 30IP

Simple interest rate $=R=4.52\%$

Explanation of Solution

Given information:

Principal amount $=\$15,000$

Time $=18$ months.

Each month she makes $\$56.50$ in interest.

Concept:

  $I=prt$

Where

  $I=$ Simple interest.

  $p=$ Principal amount

  $t=$ time in years.

  $r=$ Annual interest rate.

Calculation:

From given information

Principal amount $=p=\$15000$

Time $=18$ months.

We know

  $1$ year $=12$ months

Using that

We can say

Time $=\frac{18}{12}=\frac{3}{2}$ years.

Each month she makes $\$56.50$ in interest.

Therefore,

Total amount of simple interest $=56.5\times 18$

  $\Rightarrow$ Total amount of simple interest $=I=\$1017$

On substituting values in above mentioned concept

We get

  $\begin{array}{l}I=prt\\ \Rightarrow 1017=\left(15000\right)\left(r\right)\left(\frac{3}{2}\right)\\ \Rightarrow 1017=22500r\\ \Rightarrow r=\frac{1017}{22500}\\ \Rightarrow r=0.0452\end{array}$

We know

  $\begin{array}{l}r=\frac{R}{100}\\ \Rightarrow R=100r\\ \Rightarrow R=100\left(0.0452\right)\\ \Rightarrow R=4.52\%\end{array}$

Therefore,

To nearest cent, Simple interest rate $=R=4.52\%$