Question

A local finance company quotes a 17 percent interest rate on one-year loans. So, if you borrow $20,000, the interest for the year will be $3,400. Because you must repay a total of $23,400 in one year, the finance company requires you to pay $23,400/12, or $1,950.00, per month over the next 12 months.
1. Is this a 17 percent loan?
2. What rate would legally have to be quoted?
3. What is the effective annual rate?

Answer 1

Answer:

1. Is this a 17 percent loan?

• No, the loan charges a much higher interest rate

2. What rate would legally have to be quoted?

• 30%

3. What is the effective annual rate?

• 34.49%

Explanation:

effective annual rate = (1 + i/n)ⁿ - 1

using a financial calculator, i = 30% (PV = 20,000, PMT = -1,950, Nper = 12, FV = 0)

monthly interest rate = 2.5%

effective annual rate = (1 + 0.30/12)¹² - 1 = (1 + 0.025)¹² - 1 = 1.3449 - 1 = 0.3449 = 34.49%

APR (legal rate) = 2.5% x 12 = 30%