Question

a car dealer offers you a choice of 0% financing for 60 months or 2500 cash back on a new vehicle. You have a pre-approved 60 month loan you can use from your credit union at a 4% interest rate. f the monthly payments at 0% are 16.67 per 1000 financed, and the monthly payments at 4% are 18.41 per 1000 financed, what is the range of new car prices for which the cash back option will cost you less? For what range of car prices should you take the 0% financing?

Answer 1

To determine the range of car prices for which the cash-back option will cost less, we need to find the total cost of each option over 60 months for different car prices and compare them. Let's assume the car price ranges from $20,000 to $30,000.

For the 0% financing option, the monthly payment is $16.67 per $1,000 financed, so the monthly payment for a car priced at $20,000 would be:

$20,000 / 1000 * $16.67 = $333.40 per month

Similarly, the monthly payment for a car priced at $30,000 would be:

$30,000 / 1000 * $16.67 = $500.10 per month

Over 60 months, the total cost for the 0% financing option for a car priced at $20,000 would be:

$333.40 * 60 = $20,004

And the total cost for a car priced at $30,000 would be:

$500.10 * 60 = $30,006

For the cash-back option, the cost of the car would be reduced by $2,500, so the total cost over 60 months for a car priced at $20,000 would be:

($20,000 - $2,500) + ($18.41 * $20) * 60 = $19,484

And the total cost for a car priced at $30,000 would be:

($30,000 - $2,500) + ($18.41 * $30) * 60 = $29,222

To find the range of car prices for which the cash back option will cost less, we need to compare the total cost of each option. Setting the two equations equal to each other and solving for x, we get:

($x - $2,500) + ($18.41 * $x) * 60 < $20,004

($x - $2,500) + ($18.41 * $x) * 60 > $30,006

Simplifying, we get:

$17.285x < $22,504

$17.285x > $34,256

Dividing by 17.285, we get:

$1,300.90 < x < $1,978.63

So, for car prices between $13,000.90 and $19,978.63, the cash-back option will cost less.

To find the range of car prices for which the 0% financing option is a better choice, we can simply look at the range of car prices for which the cash-back option is more expensive, which is anything outside of the range of $13,000.90 to $19,978.63. Therefore, for car prices outside of this range, the 0% financing option is the better choice.