A loan company charges $20 interest for a two-month loan of $325. Find the annual interest rate (APR) they are charging.
Round your answer to the nearest tenth of a percent.
I = Po*r*t = $20.
325*(r/12)*2 = 20.
325*r/6 = 20.
325r = 120.
r = 0.369 = 36.9% APR.
To find the annual interest rate (APR), you need to first calculate the total interest charged for a year and then express it as a percentage of the loan amount.
1. Start by finding the monthly interest rate. Since the loan is for two months and the interest charge is $20, we can calculate the monthly interest rate using the formula:
Monthly interest rate = (Interest charged / Loan amount) * 100
= ($20 / $325) * 100
= 6.1538
2. Next, calculate the annual interest rate by multiplying the monthly interest rate by 12 since there are 12 months in a year:
Annual interest rate = Monthly interest rate * 12
= 6.1538 * 12
= 73.8462
3. Finally, round the annual interest rate to the nearest tenth of a percent:
Rounded annual interest rate = 73.8%
Therefore, the loan company is charging an annual interest rate (APR) of 73.8%.
To find the annual interest rate (APR) charged by the loan company, we need to calculate the interest rate on a yearly basis.
The first step is to determine the total interest paid for a two-month loan. It is given that the loan company charges $20 interest for a two-month loan of $325.
Next, we need to calculate the monthly interest rate. Since the loan term is two months and the total interest paid is $20, we can divide the total interest by the number of months to find the monthly interest rate:
Monthly interest rate = Total interest / Loan term
Monthly interest rate = $20 / 2 months
Monthly interest rate = $10
Now, multiply the monthly interest rate by 12 to find the annual interest rate:
Annual interest rate = Monthly interest rate * 12
Annual interest rate = $10 * 12
Annual interest rate = $120
Finally, to express the annual interest rate as a percentage, divide the annual interest rate by the loan amount and multiply by 100:
APR = (Annual interest rate / Loan amount) * 100
APR = ($120 / $325) * 100
APR ≈ 36.9%
Therefore, the annual interest rate (APR) charged by the loan company is approximately 36.9%.