Assessing the Use of Technology and Using Technology to Assess

A Case Study

Alex Heidenberg
Michael Huber

Department of Mathematical Sciences
The United States Military Academy
West Point, New York

Appendix B      Example Day Two Exam

Take Home Scenario

     While home on Spring Break, you explain to your parents the fundamental concepts that you have learned in your Discrete Dynamical Systems course.  Following dinner one evening you provide them a quick 10 minute presentation on how you were able to use DDS to assist with car buying decisions.  Due to your improved ability to communicate about mathematics, your parents immediately say, "Hey, I think you might be able to help us".  They share with you the fact that they are negotiating the purchase of a 2003 Toyota Camry.  The Wasko Federal Credit Union has agreed to finance a vehicle loan of up to $20,000 at a yearly interest rate of 6%.

Adapted Scenario

     Recall from the read-ahead that your parents have asked for your assistance to help them determine the financing option for their purchase of a 2003 Toyota Camry.  They have successfully negotiated a price of $18,000 for the car.  In order to boost slumping car sales, the dealer has offered two financing options. 

1. In Option One the dealer has offered to finance the car at a rate of 1.9% interest for 48 months.  Develop a model that predicts the car loan balance after n months, given the loan requires 48 equal payments of p dollars. Define all variables, state the domain, and any initial conditions. 
2. Determine the payment p, to the nearest cent, if your parents bought the Camry using the 1.9% loan financed by Toyota?  Explain how you used technology to obtain this figure.  Include the actual formulas used in EXCEL or the TI-89.
3.  In Option Two, the dealer has offered a $1500 rebate in lieu of the 1.9% financing.  The finance rate for this option is 5.2% interest over 48 months.  Develop a model that predicts the car loan balance after n months, given the loan requires 48 equal payments of q dollars.  Define all variables and state the domain, and any initial conditions.   
4.  Should your parents take the 1.9% financing or the $1500 rebate with a 5.2% financing rate?  Explain how you used technology to assist in your decision.  Provide clear mathematical backing to support your decision.    Include the actual formulas used in EXCEL or the TI-89.