Question

Suppose you secure a home improvement loan in the amount of $7,000 from a local bank with an add-on rate of 15% for two years. You will make 24 equal monthly payments.

(a) Determine the amount of the monthly installment.

(b) Compute the nominal and the effective annual interest rate on the loan

Answer 1

a) Loan amount = $7,000

Add on rate = $15% for 2 years

Interest = 7,000 * 0.15 * 2 = 2,100

Total repayment = 7,000 + 2,100 = 9,100 in 24 payments

Monthly payment = 9,100 / 24 = 379.17

b) Formula to calculate EMI = [Loan amount * r * (1 + r)^ⁿ] / [(1 + r)^ⁿ - 1]

where r is rate of interest and n is number of payments

379.17 = [7,000 * r * (1 + r)^{^24}] / [(1 + r)^²⁴ - 1]

By approximation, r = 2.22%

Annual effective rate of interest: {[1 + 2.22%]^¹² - 1} * 100 = 30.15%