Word Problem on Finance

Topic : Finance

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. If 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?

Solution :
Let the price at which both the options will give same result be x thousand (dollor)
Total payment for cash purchase,
= 16.67 x.60
and total payment for credit purchase
=18.41x.60 - 2500
Since these are supposed to be equal,
18.41x.60-2500=16.67x.60
1104.6x-2500=1000.2x
-1000.2x = -1000.2x
------------------------
104.4x-2500=0
+2500=+2500
-----------------
104.4x=2500
x=2500/104.4
x= 23.946
So below 23.946thousand = $23.946, the cash back option will cost less.
Above $23.946 you should take 0% financing