Question

A loan of $20,000 was offered for 24 months. Monthly payments are $1118.

What is the loan's monthly interest rate?

What is the loan's annual effective interest rate?

Please show all the work including any equations used.

Answer 1

(I)

Let monthly interest rate be r%. Then

Monthly payment = Loan amount / P/A(r%, N)

1,118 = 20,000 / P/A(r%, 24)

P/A(r%, 24) = 17.8891

From P/A factor table we find: P/A(2%, 24) = 18.9139 and P/A(3%, 24) = 16.9355.

So,

2% < r < 3%

Using interpolation,

(r - 2) / (3 - 2) = (17.8891 - 18.9139) / (16.9355 - 18.9139)

(r - 2) / 1 = - 1.0248 / - 1.9784

r - 2 = 0.52

r = 2.52%

(II)

Number of months per year = 12

Effective annual rate = (1 + 0.0252)¹² - 1 = (1.0252)¹² - 1 = 1.3480 - 1 = 0.3480 = 34.80%