Question

To finance the purchase of some computer equipment and software for your consulting company, you are taking out a $24,000 loan today. The interest rate on the loan is 3.5% annual percentage rate compounded monthly. You will make monthly payments to the bank to pay off this loan over 5 years.

(a) (9 pts) What is the amount of your equal monthly payment?

(c) (6 pts) How much money would you need if you want to pay off this loan at the end of the 15th month (assume you will pay the 15th payment and then pay off the rest of the loan)?

Answer 1

We need to apply the PV of annuity concept in this question, which is mathematically shown as:

For our question, PV = $24,000, r = 3.5%/12 = 0.2917% (monthly rate), n = 5 * 12 = 60 months

24000 = P * 54.97

P = $436.60 ---> Monthly Payment

c) In order to calculate the amount of money to be repaid after 15 months in order to extinguish the loan, we simply need to calculate the PV of equal monthly payments remaining (over next 45 months).

PV = 436.6019 * 42.1145

PV = $18,387.27 --> Answer