Question

Your friend borrows $100 from you and promises to pay you back $109 in 8 months. What annual percentage rate (A.P.R.) are you charging your friend? Round to the nearest tenth of a percent and write the answer as a decimal

Answer 1

Answer:

$12.0\%=0.12$

Step-by-step explanation:

We have been given that your friend borrows $100 from you and promises to pay you back $109 in 8 months.

We will use simple interest formula to solve our given problem.

$A=P(1+rt)$, where,

A = Amount after t years,

P = Principal amount,

r = Annual interest rate in decimal form,

t = Time in years.

Convert 8 months to year:

$\frac{8}{12}\text{ year}=\frac{2}{3}\text{ year}$

$108=100(1+r*\frac{2}{3})$

$108=100+r*\frac{2}{3}\times 100$

$108-100+r*\frac{200}{3}$

$108-100=100-100+r*\frac{200}{3}$

$8=r*\frac{200}{3}$

$8\times \frac{3}{200}=r*\frac{200}{3}\times \frac{3}{200}$

$\frac{24}{200}=r$

$r=\frac{24}{200}$

$r=0.12$

Convert to percent:

$0.12\times 100\%=12\%$

Therefore, you are charging 12% APR to you friend.