Calculating a Car Payment
Grade Level: 9 - 12
by Barbara Christopher

Background needed:

    The student should have knowledge of complex fractions
    and large exponents.

Objectives:

    1. The student will use a formula containing complex fractions and large exponents to calculate a monthly car payment.
    2. The student will use the order of operations while putting such a formula into a scientific calculator.
    3. The student will see a very practical use for complex fractions and large exponents.

Materials:

    1. Access to the Internet
    2. A simple scientific calculator

Procedure:

    In this lesson, students will choose a car from an Internet used car dealer and then calculate their monthly payment. To reach the service, have students type in the URL below for the autobytel.com Used Car Purchase Center

    http://www.autobytel.com/content/buy/UsedIndex.cfm?id=4

    Once they reach autobytel.com students will pass through several pages as they find the right car and the right price for them. When they have found their price, have them experiment with different interest rates and numbers of payments in the formula below.

    In this formula for a monthly payment, assume that there is no down payment and that the student must finance the entire price of the car. The formula has a principal, P, interest rate, r, and number of monthly payments, m.

                        P ( r / 12 )
                  -------------------------
                                       -m 
      	        (1 - ( 1 + r / 12 )   )
    

    For example, a 3 year (36 month) loan of $15,000 at 7% interest would look like this:

                      15000 ( 0.07/ 12 )
                 ------------------------------
                                          -36
                    (1 - ( 1 + 0.07 / 12 )    )
    

    The payment for this car will be $463.16 per month.

    Have students write down the setup for first a 3 year and then a 4 year 7% loan, and enter it in the calculator. Next have them calulate a 3 year loan at 6%.

    The setup should be a step-by-step list of how the numbers and parentheses are to be entered into the calculator and which buttons must be pressed at which point. Warn them that the fraction bar is a grouping symbol and that parentheses are sometimes needed to separate the numerator and denominator of a complex fraction.

Sites that list this lesson and ones like it:

This page was developed through TeacherTECH, a teacher training and student technology council program sponsored by the Center for Excellence and Equity in Education (CEEE)

Copyright August, 1997 Barbara Christopher

Comments and suggestions ?