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

`12.0\%=0.12`

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:

`(8)/(12)\text{ year}=(2)/(3)\text{ year}`

`108=100(1+r*(2)/(3))`

`108=100+r*(2)/(3)* 100`

`108-100+r*(200)/(3)`

`108-100=100-100+r*(200)/(3)`

`8=r*(200)/(3)`

`8* (3)/(200)=r*(200)/(3)* (3)/(200)`

`(24)/(200)=r`

`r=(24)/(200)`

`r=0.12`

Convert to percent:

`0.12* 100\%=12\%`

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