A vehicle owner wants to calculate the total cost of his 200

A vehicle owner wants to calculate the total cost of his 2007 Jeep Compass with a MSRP of $18,366. His monthly loan payment is $317.54 for 5 years after he puts down a $2000 down payment.†

(a) Write a formula for the total amount he has paid toward the cost of the car (including down payment), T, as a function of the number of months he has made payments on the loan, m. T(m) =

(b) What is the total cost of the Jeep, after he has made all of the payments? $

(c) How much money has he paid in interest for his Jeep? $

Solution

Solution:

m = number of months he has made payments on the car

T(m) = total amount paid after m months

a)

The states that he makes a loan payment of $317.54 every month.

It also states that he made a $2,000 down payment.

Therefore the formula is

T(m) = 317.54m + 2000

This means that at m = 0 months, the total paid is just the down payment ($2,000), which makes sense.

After 1 month (m = 1), the total is the down payment plus 1 month\'s payment of $317.54.

b)

The loan amount is for 5 years.

Since there are 12 months in a year, that\'s a total of 12*5 = 60 payments he\'ll be making.

The total cost of the car will be figured out when m = 60.

T(60) = 317.54*60 + 2000 = $21,054.2

c)

The interest paid will be the total amount he\'s paid on the car minus the MSRP (i.e. how much it would have cost if

he had just paid cash upfront).

Interest paid = Total Paid - MSRP = $21,054.2 - $18,366.00 = $2,688.2

For paying off the car in small increments over a long period of time,

he wound up shelling out almost $2,700 extra in interest.