Question

A student borrowed $8600 from the bank. She must pay $300 at the end of every month for 5 years. What is the effective annual interest rate on the loan?

Answer 1

Number of months = 5 x 12 = 60

Monthly loan repayment = Loan amount / P/A(r%, 60) where r: Nominal monthly interest rate

$300 = $8600 / P/A(r%, 60)

P/A(r%, 60) = $8600 / $300 = 28.6667

From P/A Factor table we find: P/A(2%, 60) = 34.7609 and P/A(3%, 60) = 27.6756

Therefore, 2% < r < 3%. Using interpolation,

(r - 2)% / (3 - 2)% = (28.6667 - 34.7609) / (27.6756 - 34.7609)

(r - 2)% = -6.0942 / -7.0853

r - 2% = 0.86

r = 2.86%

Effective annual interest rate = (1 + 0.0286)¹² - 1 = (1.0286)¹² - 1 = 1.4027 - 1 = 0.4027 = 40.27%