Question

Samantha borrowed money to buy lawn equipment to start her new lawn service business. She borrowed $800 for 9 months and paid $70.50 in interest. What was the rate of interest?

Answer 1

The rate of interest for the amount borrowed by Samantha is 11.75 %

Solution:

Given, Samantha borrowed money to buy lawn equipment to start her new lawn service business.

She borrowed $800 for 9 months and paid $70.50 in interest.

We have to find what was the rate of interest?

Now, amount = $800, simple interest = $70.5, time period = 9 months =
`(9)/(12) = (3)/(4) years.`

Simple Interest is given as:

`\text { simple interest }=\frac{\text { amount } * \text { interest rate } * \text { time period }}{100}`

`\begin{aligned} \text { Then, } 70.5 &=\frac{800 * \text { rate} * (3)/(4)}{100} \\\ & \rightarrow 800 * \text { rate } * (3)/(4)=7050 \end{aligned}`

`\begin{array}{l}{\rightarrow \text { Rate } * 3 * 200=7050} \\\\ {\rightarrow \text { Rate } * 600=7050} \\\\ {\rightarrow \text { Rate }=(7050)/(600)} \\\\ {\Rightarrow \text { Rate }=11.75 \%}\end{array}`

Hence, the interest rate is 11.75%.