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?

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%

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%

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