Question

The cash price of a new automobile is 10,000. The purchaser is willing to finance the car at 18% convertible monthly and to make payments of 250 at the end of each month for 4 years. Find the down payment which will be necessary.

Answer 1

Answer: $1,489

Explanation:

The down payment will be the difference between the cash price of $10,000 and the present value of the $250 payments at the end of each month for 4 years.

Period = 4 * 12 months = 48 months

Interest = 18/12 = 1.5%

Present value = 250 * $\frac{1 - ( 1 + r)^{-n} }{r} = 250 * \frac{1 - ( 1 + 0.015)^{-48} }{0.015}$

= 250 * 34.04255364558839163

= $8,510.64

= $8,511

Down payment = 10,000 - 8,511

= $1,489