Question

A local finance company quotes an interest rate of 19.9 percent on one-year loans. So, if you borrow $48,000, the interest for the year will be $9,552. Because you must repay a total of $57,552 in one year, the finance company requires you to pay $57,552/12, or $4,796.00 per month over the next 12 months.

Required:
a. What rate would legally have to be quoted?
b. What is the effective annual rate?

Answer 1

a. What rate would legally have to be quoted?

• banks are required to quote the APR, which in this case is 19.9%

b. What is the effective annual rate?

• 22.1%

Step-by-step explanation:

Annual percentage rate (APR) = [($9,552 / $48,000) / 365] x 365 x 100 = 19.9%

In this case, you should only divide $9,552 / $48,000 and then multiply by 100 since the loan only lasts one year.

effective annual rate = (1 + 0.199/365)³⁶⁵ - 1 = 0.2201 = 22.1%