Question

Hoyt Axton earned $244.80 interest in 9 months from an investment that paid 3.2% per year. Use the simple interest formula to find the amount initially invested

Answer 1

Solution:

Given:

$\begin{gathered} \text{Interest,I}=\text{ \ 244.80} \\ \text{Time,T}=9\text{months} \\ But\text{ 12months=1year} \\ T=\frac{9}{12}\text{years} \\ \text{Rate,R}=3.2\text{ \%} \end{gathered}$

We need to get to the principal.

$I=\frac{P\times T\times R}{100}$

Substituting these values into the formula;

$\begin{gathered} 244.80=\frac{P\times\frac{9}{12}\times3.2}{100} \\ Cross\text{ multiplying;} \\ 244.8\times100=P\times\frac{9}{12}\times3.2 \\ 24480\times12=P\times9\times3.2 \\ 293760=28.8P \\ \text{Dividing both sides by 28.8,} \\ \frac{293760}{28.8}=P \\ P=\text{ \ 10,200} \end{gathered}$

The amount initially invested is known as the Principal.

Hence, the principal is $10,200