Instructions:

Use the formulas for compound interest and amortizations to help you answer the questions below. As you work through the problems, try to spot the patterns that emerge to help you answer the discussion questions in the final step of this project.

You will work on this assignment as a group. You can divide and conquer parts of this assignment. For instance, you could assign some members of your group to find a car while other members of your group find two loans. You could also separate out the work of calculating compound interest and the amortization of the loan. However, the group should work together to answer the discussion questions. The file for this project can be downloaded here: 14-1 Buying a Car.docx

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Variables and Formulas

Variable	Symbol	Explanation
Amount (Final)	A	The amount of money paid back at the end of a given loan
Principal	P	The amount of money borrowed at the start of an investment
Interest	I	The amount of money paid for the privilege of borrowing the principal
Interest Rate	r	The percentage of the principal that is turned into interest on an annual basis
Time	t	The time, measured in years, that the money is borrowed before being paid off
Compound Rate	n	The number of times per year that the interest is recalculated
Periodic Payment	M	The amount of money that is paid, typically monthly, on a regular basis into the loan

Model Formula

Model	Formula
Final Amount	A=P+I
Compound Interest	A=P(1+rn)nt
Amortization: Monthly Payment	M=Prn1(1+rn)nt
Maximum Loan	P=M1(1+rn)ntrn

Step 1: Finding a Car

Search on the Internet for a car that you would like to purchase. Complete the following:

1. Asking price:
2. Car make, model, year, color:
3. Picture of the car:

Note: Please do not submit personal information just to answer this assignment. There are lots of sites, which will let you browse their offerings without giving them personal information.

Step 2: Finding a Loan

Different lengths of loans have different interest rates. Use the Internet to identify two loan options with different lengths of loans for purchasing your vehicle.

Complete the table with the information for your loans:

Lender	Length of loan in months	APR

1. Which loan do you think will result in you having to pay back the most interest?
2. What is it about the loan that makes you think this way.

Step 3: Repaying the Car Loan

Using the information that you gathered in Steps 1 & 2:

1. Find the monthly payment for the first loan.
   1. How much will you pay in total for the car?
   2. How much total will you pay in interest?

2. Find the monthly payment for the second loan.
   1. How much will you pay in total for the car?
   2. How much total will you pay in interest?

Step 4: Making a down payment

Often, people who purchase cars put some money down either in the form of cash up front or trading in a used car.

1. Calculate a 5% down payment
2. What is the amount you need to borrow to purchase your car?
3. Find the monthly payment for the first loan.
   1. How much will you pay in total for the car?
   2. How much total will you pay in interest?
4. Find the monthly payment for the second loan.
   1. How much will you pay in total for the car?
   2. How much total will you pay in interest?