Lower Car Payment

The Effect of Extending the Loan Term on Monthly Payment and Total Cost

This assignment is on low car payment when you go to buy a car, you may have the opportunity to have a lower car payment by extending the length of the loan.But how much is this lower payment really costing? In this sheet you will fill in some tables that deal with different interest rates that illustrate what effect a lower monthly payment has on both the term of a loan and the total cost of the loan.

A:  amount for a car loan, the total amount left to finance after all charges and the down payment

t:  the term of the car loan in years, the number of years it will take to pay off the car loan

r:  nominal yearly interest rate on the car loan

(Note:  Recall that since interest is compounded monthly, the formula for the effective rate is given by eff. rate  =   – 1.)

P:  your monthly payment on the car loan

C:  total cost of the loan, the total amount it costs you to pay back your loan

I:  total interest on your loan.

Since interest on car loans is compounded monthly, the monthly payment P for a loan of amount A over a length of t years at a nominal yearly interest rate of r can be found using the formula

(1) .(Do not do any rounding until you get P.  P should be the first thing you round, and you should round it to the nearest cent.)Since there are 12 months, and therefore 12 monthly payments each year; the total cost of the loan over the t years will be

(2) C = 12tP,and the total interest you paid on the loan will be

(3) I = C – A.

Example 1: Suppose you are financing $14,000 on a car at an interest rate of 9%.  Find the monthly payment, the total cost of the loan, and the total interest on the loan if you choose to finance the car over 2 years b. 5 years:

Exercise 1:  Complete the following table, which investigates the effect that changing the length of a loan has on the monthly payment, the total cost of the loan, and the total interest paid on the loan.  (The first and last columns have been filled in using information from Example 1, which you can use to make sure that you are doing your calculations correctly.)

Exercise 2:  Complete the following table, which investigates the effects that the interest rate and the length of the loan have on the monthly payment for the loan, the total cost of the loan, and the total interest on the loan:

Equation (1) above allows us to find the monthly loan payment P given the amount of the loan A, the nominal yearly interest rate r, and the term (length) of the loan t.  Suppose though that after making your budget, you feel that you can afford (after setting aside money for tithe, savings, vehicle maintenance, licensing, etc.) a monthly car payment of P.  If we solve Equation (1) for A, we get

(4) .Example 2:  After doing your budget, you find that you can set aside $350 each month for car purchasing a car.  How much of a loan can you take out at an interest rate of 9% if you want the term of the loan to be:

2 years b. 2years = $7,661.20 = $9371.28

Exercise 3:  Complete the following table, which investigates the effect changing the length of a loan and the nominal yearly interest rate has on the amount that can be borrowed: