Answer:
[tex]12.0\%=0.12[/tex]
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.
[tex]A=P(1+rt)[/tex], 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:
[tex]\frac{8}{12}\text{ year}=\frac{2}{3}\text{ year}[/tex]
[tex]108=100(1+r*\frac{2}{3})[/tex]
[tex]108=100+r*\frac{2}{3}\times 100[/tex]
[tex]108-100+r*\frac{200}{3}[/tex]
[tex]108-100=100-100+r*\frac{200}{3}[/tex]
[tex]8=r*\frac{200}{3}[/tex]
[tex]8\times \frac{3}{200}=r*\frac{200}{3}\times \frac{3}{200}[/tex]
[tex]\frac{24}{200}=r[/tex]
[tex]r=\frac{24}{200}[/tex]
[tex]r=0.12[/tex]
Convert to percent:
[tex]0.12\times 100\%=12\%[/tex]
Therefore, you are charging 12% APR to you friend.
