Question

A car costing $32,500 can be purchased today by paying a $5,000 deposit and no payments for six months. The purchase contract states that you must make your first payment seven months from now and this would continue for a total of 36 monthly payments. What would be the the amount of each payment payable to the car dealer if they will charge interest at 12% p.a. compounding semi-annually?

Answer 1

Since the payments are monthly, convert the 12% pa compounded semi annual rate into compunded monthly annual rate.

(1+i)^12 - 1 = (1+r/2)^2 - 1

Here r = 12%

(1+i)^12 = (1+6%)^2

(1+i) = (1+6%)^(1/6)

i = (1+6%)^1/6 - 1

i = 0.98%

Initial cost of car = $32,500

Deposit = $5,000

Remaining amount payable = $32,500 - $5,000 = $27,500

Amount payable after six months = P(1+i)^6

Amount payable after six months= 27,500 (1+0.98%)^6

Amount payable after six months = $ 29,150

Now there are 36 monthly payments to be made at the end of every month whose PV is equal to $29,150

Let the equal monthly payment is x

x/(1+0.98%)^1 + x/(1+0.98%)^2 +x/(1+0.98%)^3...............x/(1+0.98%)^36 = 29,150

x = $964.17

So each amount payable to car dealer is $964.17