Developed by QR Fellow Elizabeth Vidaurre

**Objective**: Students will learn to gather necessary information to interpret a problem. In addition, the *main learning objective is that* students will be able to identify the mathematical relationship between various quantities in order to look back and answer the question “does this answer make sense?” After learning to make necessary calculations for amortization tables, they will then make decisions based on analytical reasoning. By extension, students will learn how to use interest rates in financial situations.

**Background:** Ask students to pick their dream car and find out how much it costs. Also, have them read http://usnews.rankingsandreviews.com/cars-trucks/How-to-Finance-a-Car. This website also has a lot of useful information, but is much longer http://auto.howstuffworks.com/buying-selling/car-financing1.htm.

**Activity:**

Part 1: Test students on their general understanding with the following questions (do not give the answers to questions 4 & 5 until after the activity):

- Should you finance your car through the dealer? How does the dealer profit from you financing your car?
- Should you put as much money down as you can?
- Is it better to have a higher or lower interest rate?
- Is the lender more likely to give you a lower interest rate if your loan term is longer or shorter?
- If the monthly payment is higher, will the loan term be lower or higher?
- If the loan term goes up, will the amount of interest paid go up or down?
- If you have a low credit score, what might the lender do?
- What is a good enough credit score?
- What do the words loan principal, loan term, APR and amortization mean?

Part 2: Now they can actually get their hands dirty with some numbers.

- Using one of the methods in http://www.wikihow.com/Calculate-Loan-Payments , have students calculate their monthly payments for an interest rate of 6% and an interest rate of 10%. (Depending on the level of the course, it might be instructive to have students derive the formula for monthly payments, use it and then use the online calculators for verification). Have them fill out the following amortization tables:

Term of the loan | Monthly payment | Total payment after term of the loan | Total interest paid |

60 months | |||

48 months | |||

36 months | |||

24 months | |||

12 months |

Term of the loan | Monthly payment at 6% interest | Monthly payment at 10% interest | Monthly saving |

60 months | |||

48 months | |||

36 months | |||

24 months | |||

12 months |

- Ask the students to find out how much they save and how much sooner their loan would be paid off if they add $50 to their monthly payment. This can be done with a table.
- Have students reassess their answers to questions 4 and 5.

**Suggested Solutions:**

- You should apply to various places and get the best deal possible. Avoid offers that charge you a lot of fees. Another thing to look at is the car loan term. A longer auto loan might result in a lower monthly payment, but over the long haul, you’ll pay more in interest. Also, watch out for loans that have a prepayment penalty, which is a fee charged if you pay the loan off early.
- Yes, unless you can find an interest rate that is lower than inflation.
- Lower
- Shorter
- Lower
- Up
- Require a higher down payment or a higher interest rate
- 720
- Loan principal: amount borrowed

Loan term: amount of time you have to pay the lender back

APR: annual percentage rate

Amortization: rate at which the initial amount borrowed (the principal) is reduced

**Download Activity: **

Word Document: Car loans

**References:**

http://seceij.net/seceij/winter12/incorporating_q.html