Question

You are going to take a loan of $100,000 from a local microfinance institute to repay in 12 equal installments. The institute deducts 10% as a fixed deposit at the time when you take the loan. Your installment per month is $10,155. How much interest are you paying? [Hint: calculate the interest rate per period and multiply it by 12]

(I must solve the problem on paper with a formula, not on Excel) Thank you!

Answer 1

Using present value of annuity formula, we can calculate the interest rate on loan.
Present value of annuity = P*{[1 - (1+r)^-n]/r}
Present value of annuity = Actual loan disbursed = $100000 - (10% of $100000) = $90,000
P = monthly loan installment = $10155
r = monthly interest rate = ?
n = number of loan installments = 12
90000 = 10155*{[1 - (1+r)^-12]/r}
8.862629 = [1 - (1+r)^-12]/r
r = 0.05
Monthly interest rate = 5%
Interest rate you are paying = 5% * 12 = 60%