Question

Mas Joko bought a used car for $ 3,000. He made payments on the car by going into debt to the bank in installments every month for 12 months, starting from the first month after he bought the used car. The bank provides compound interest of 12% per month. After making 6 installment payments, Mas Joko decided to resell the used car. A prospective buyer is willing to pay for the car by paying the remaining debt plus $ 1,000 in cash to Mas Joko. If Mas Joko is always on time to pay his 6 installments, and there is no penalty given by the bank to Mas Joko, what is the price of a used car paid by the prospective buyer?

Answer 1

Price of car (P) = 3,000 which is paid in equal installments in 12 (n) months at an interest rate of 12% (r) per month

Installment per month = [P * r * (1 + r)^ⁿ] / [(1 + r)^ⁿ - 1] = [3,000 * 0.12 * (1 + 0.12)^¹²] / [(1 + 0.12)^¹² - 1] = 484.31

After making six payments of 484.31 each:

Present value of amount paid is calculated as: [Amount / (1 + Rate of Interest)^^{Months pending to clear the loan}]

Payment No.	Amount	Present value
1	484.31	124.31
2	484.31	139.23
3	484.31	155.93
4	484.31	174.65
5	484.31	195.60
6	484.31	219.08
		1,008.80

present value of first 6 payments is 1,008.80 which means Mas Joko have paid 1,008.80 of prinicipal amount out of 3,000 in first 6 months. Remaining debt = 3,000 - 1,008.80 = 1,991.20

Buyer paid 1,000 + 1,991.20 = 2,991.20 to Mas Joko to buy the car.