Chapter 6.6, Problem 16IP

To determine

To find: Simple interest rate.

Answer to Problem 16IP

Simple interest rate $=R=4\%$

Explanation of Solution

Given information:

Principal amount $=\$4800$

Time $=60$ months.

He will be paying $\$96$ each Month.

Concept:

  $I=prt$

Where

  $I=$ Simple interest.

  $p=$ Principal amount

  $t=$ time in years.

  $r=$ Annual interest rate.

Calculation:

From given information

Principal amount $=p=\$4800$

Time $=60$ months.

We know

  $1$ year $=12$ months

Using that

We can say

Time $=5$ years.

He will be paying $\$96$ each Month.

Total amount he paid $=96\times 60$

  $\Rightarrow$ Total amount he paid $=\$5760$

Simple interest $=I=5760-4800$

  $\Rightarrow I=\$960$

On substituting values in above mentioned concept

We get

  $\begin{array}{l}I=prt\\ \Rightarrow 960=\left(4800\right)\left(r\right)\left(5\right)\\ \Rightarrow 960=24000r\\ \Rightarrow r=\frac{960}{24000}\\ \Rightarrow r=0.04\end{array}$

We know

  $\begin{array}{l}r=\frac{R}{100}\\ \Rightarrow R=100r\\ \Rightarrow R=100\left(0.04\right)\\ \Rightarrow R=4\%\end{array}$

Therefore,

To nearest cent, Simple interest rate $=R=4\%$