Question

What annual rate of interest would you have to earn on an investment of \(3500 to ensure receiving \)262.50 interest after 1 year?

Short answer

The annual rate will be 7.5%to earn on an investment of $3500 to ensure receiving $262.50 interest after 1 year.

Step-by-step solution

Step 1. Definition of simple interest formula.

A simple interest is a method of calculating interest based on the original amount invested or loaned called the principal. The annual interest is given bywhere P is the principal amount invested or borrowed, r is the interest rate andt is the number of years elapsed.

Step 2. Make the equation.

We have,

Principal amount:$P=\$3500$

Interest:$I=262.50$

Time:$t=1\text{year}$

Plug the value in the simple interest formula:

$\begin{array}{l}I=Prt\\ 262.50=3,500\left(r\right)\left(1\right)\end{array}$

Step 3. Solve the equation.

We have,

$\begin{array}{l}262.50=3,500\left(r\right)\left(1\right)\\ 262.50=3,500r\end{array}$

Divide both sides by 3500:

$\begin{array}{l}\frac{262.50}{3500}=\frac{3,500r}{3500}\\ r=0.075\end{array}$

Now, multiply 0.075 by 100 to convert into a percentage:

$\begin{array}{l}r=0.075\times 100\%\\ r=7.5\%\end{array}$

Hence, the annual rate is 7.5%.