You are buying a car for $38713. your payments are $774 per month and you put $2500 as a down payment. you finance the car for 5 years. at the end of 12 years, your car will depreciate to zero. calculate the number of months it will take your car to equal the value of your payments.

37.12 mo

Step-by-step explanation:

Your total payment (P) starts at zero and increases by $774 each month. Thus, the formula for your total payment is

P = 774t

where t is the number of months.

The value (V) of your car starts at $38 713 and decreases to zero over 12 yr (144 mo) .

The monthy rate of depreciation is $38 713/144 mo = $268.84/mo.

So, the equation for the value of your car is

V = 38 713 – 268.84t

The value of your car will equal your total payments when

           P = V     Substitute the expressions for P and V

      774t = 38 713 – 268.84t     Add 268.84t to each side

1042.84t = 38 713                      Divide each side by 1042.84t

            t = 37.12 mo

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You can see what’s happening in a graph of the two functions.

The blue line represents the depreciating value of your car. It starts at

$38 713 when new and decreases to $25 271 after 50 mo.

The red line represents your total payments. They start at zero and increase to $38 700 after 50 mo.

The two lines intersect at (37.12, 28 733).  At that point, the value of your car equals your total payments.

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