Question

A man needed money for college. He borrowed $5,000 at 16% simple interest per year. If he paid $200 interest, what was the duration of the loan?

Answer 1

We have a simple interest case. In this kind of situation, we have to use the next formula for simple interest:

`I=P*R*T`

Where:

• I is the earned interest. In this case, we have I = $200.

,

• P is the Principal amount (that is, the amount the man borrowed in this case). In this case, we have P = $5,000.

,

• R is the interest rate. In this case, we have I = 16% = 16/100.

,

• T is time transcurred to get the earned interest. This is the unknown value we are about to find.

Therefore, we have:

`\begin{gathered} I=\text{ \$200} \\ P=\text{ \$5,000} \\ R=(16)/(100)=0.16 \end{gathered}`

Then we have:

`200=5000(0.16)*T`

Now, we need to divide both sides of the equation by the product 5000(0.16) to solve for T as follows:

`\begin{gathered} (200)/(5000(0.16))=T \\ \\ T=(200)/(800)=0.25 \end{gathered}`