Question

What is the principal remaining after 19 monthly payments have been made on a $16000 four -year loan? The annual interest rate is 18% nominal compounded monthly.

answer: $10987

Answer 1

First, we need to find the monthly payments

There are 12 months in a year:

Number of periods = 4 * 12 = 48

Rate = 18% / 12 = 1.5%

Present value = Monthly amount * [1 - 1 / (1 + r)^n] / r

16,000 = Monthly payments * [1 - 1 / (1 + 0.015)^48] / 0.015

16,000 = Monthly payments * [1 - 0.489362] / 0.015

16,000 = Monthly payments * 34.042554

Monthly payments = 470

48 - 19 = 29

Therefore, there are 29 months remaining for the loan to complete

Principal remaining = Monthly payments * [1 - 1 / (1 +r)^n] / r

Principal remaining = 470 * [1 - 1 / (1 +0.015)^29] / 0.015

Principal remaining = 470 * [1 - 0.649359] / 0.015

Principal remaining = 470 * 23.376076

Principal remaining = $10987