Question

You are considering the purchase of a new car using a financing arrangement. Under the deal you must make a $10,000 deposit immediately and then monthly payments of $800 for a period of 48 months. The monthly payments are made at the end of each month. The interest rate is 12% p.a. compounded monthly. What is the effective cost of the car?

Answer 1

Given that interest rate i.e. r = 12% p.a. Compounding monthly i.e. 12/12 = 1% for one month

Periodic deposit at the end of the period = $800

Number of deposits i.e. n = 48

The effective cost of the car is the present value of all the payments made for the car

Since payments are at the end of each period it is a type of ordinary annuity and the present value of an ordinary annuity is:

Payment x (1-{1+r}^-n )/r

Hence present value of all the monthly payments made for 48 months is:

= 800 x (1-{1+0.01}^-48 )/0.01

= 800 x (1-0.620260405)/0.01

= 800x0.379739595/0.01

= 800 x 37.9739595

=$30379.17

Also downpayment made = $10000

Hence total effective cost of the car = $30379.17+10000

=$40379.17