Natalie purchases a new car for $26,868. She pays 3,000 up front and agrees to make a $430 payment every month for 60 month Natalie’s car loses value as it get older. A common accounting method to track this loss of the value is straight-line depreciation. According to straight-line depreciation, Natalie’s car loses $223 in value each month After how many months will the money Natalie had paid equal the value of her car?
Accepted Solution
A:
It will take 36.6 or 37 months.
We will set up an equation to represent this. Let m be the number of months. The amount of money she has paid can be represented by 3000+430m. The amount of money her car is worth can be represented by 26868-223m. Set these equal:
3000+430m=26868-223m
Add 223m to both sides: 3000+430m+223m = 26868-223m+223m 3000+653m=26868
Subtract 3000 from both sides: 3000+653m-3000 = 26868-3000 653m=23868
Divide both sides by 653: 653m/653 = 23868/653 m = 36.6