Respuesta :
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 = [tex]\frac{9}{12} = \frac{3}{4} years.[/tex]
Simple Interest is given as:
[tex]\text { simple interest }=\frac{\text { amount } \times \text { interest rate } \times \text { time period }}{100}[/tex]
[tex]\begin{aligned} \text { Then, } 70.5 &=\frac{800 \times \text { rate} \times \frac{3}{4}}{100} \\\ & \rightarrow 800 \times \text { rate } \times \frac{3}{4}=7050 \end{aligned}[/tex]
[tex]\begin{array}{l}{\rightarrow \text { Rate } \times 3 \times 200=7050} \\\\ {\rightarrow \text { Rate } \times 600=7050} \\\\ {\rightarrow \text { Rate }=\frac{7050}{600}} \\\\ {\Rightarrow \text { Rate }=11.75 \%}\end{array}[/tex]
Hence, the interest rate is 11.75%.
