Question

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.

Answer 1

Answer:

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.