Question

You are saving money to buy a Car. You will need $20,000 as the price of the car today. If you can make a down payment now of $8000 , and want to pay the rest by installments,

1. how much each deposit per month should be if you want to pay the rest of the amount in 24 months if the interest rate on the deposit is 6% per year?
2. If you can deposit $664 per month how long will it take you to pay the residual amount from the price of the car?

Please give me details and 100% right answer.

Answer 1

A. Since I have already paid $8000, the amount remaining is $12,000. Let the equal installment amount be A. The per month interest rate becomes 0.5%. So, the present value formula gives:

12000 = A/(1.005) + A/(1.005)^2 + A/(1.005)^3 + A/(1.005)^4 + ......... + + A/(1.005)^24

A = 12000/22.56 = $531.8473

B. In this question, we need to find how many months of installments we need to pay. So

12000 = 664/1.005 + 664/1.005^2 + .....+ 664/1.005^n

We have to find n. We do this by hit and trial.

We find that n=19. Hence, it will take 19 months to pay the residual amount back.