# principal amounts

Logic, Decision Making, and Introduction to Statistics

Being well informed, or at least knowing the right questions to ask, can save you from being taken advantage of. The purchase of a car involves so many variables that it is best to have some understanding before you attempt to purchase a car. There are even more variables to consider when you lease a car. For the purpose of this example, you will ignore such things as tax and dealer rebates. Research the differences between buying and leasing a car.

1. Choose a car that you wish to own, and find the price of this car. For this example, only consider new cars to purchase from a dealership. This will be your principal value, P. (3 points)

Principal,   P

\$

2. Research available interest rates on this particular car. This will be the rate, r. (3 points)

Rate in decimal form, r

3. Decide how long you would like to take to pay off this car. Choose within 2 to 5 years. This will be the time, t. (3 points)

Time,   t

? years

4. The simple interest formula, , can tell you how much interest will be added to the principal amount of this loan. Calculate the interest on your loan.

Interest,   I

\$

Show your work here: (5 points)

5. How much will you be repaying over the life of your loan?

Total   repayment

\$

Show your work here: (5 points)

6. How much are your monthly payments?

Monthly payments

\$

Show your work here: (5 points)

7. Assume that you have 6% to use as a down payment based on the original purchase price of the car. How much will you be putting down? What is the new value of P on your lease?

Down payment, D

\$

New value, P

\$

Show your work here: (7 points)

8. With the down payment, what will the new monthly payments be?

New monthly payment

\$

Show your work here: (7 points)

LEASING

Now, consider the option to lease this same car.

9. The appeal of a lease is a lower interest rate. Subtract 3% from the original interest rate (from Step 2). If your answer is less than 0.6%, use the minimum rate of 0.6%. (3 points)

Reduced rate in decimal form, r

10. The length of a lease is typically 3–7 years. Choose how long you wish to lease this car. (3 points)

Lease time, t

? years

11. The monthly payment on a lease accounts for the depreciation of the car’s value. Assume that at the end of your lease, the car has only retained 50% of its original value (50% of your answer in Step 1). What is your car’s value at the end of the lease? Use this for your new value of P.

New value, P

\$

Show your work here: (5 points)

12. How much interest will you be paying over the course of this lease?

Interest,   I

\$

Show your work here: (5 points)

13. What is your total cost—in other words principal plus interest?

Total   cost

\$

Show your work here: (5 points)

14. How much is your monthly payment?

Monthly   payment

\$

Show your work here: (5 points)

15. At the end of the lease, you do not own the car. If you wish to purchase the car, you would still owe the value of P from Step 11. At this point, you could turn in the keys and walk away, assuming the car is in perfect condition and ignoring mileage fees. What are the benefits and disadvantages to walking away from this car?

16. Instead of walking away, you could also purchase the car for what it is now worth, plus the interest. Using P from Step 11, r from Step 2, and t from Step 3, calculate how much you would repay over the course of this new loan.

Interest

\$

Total repayment

\$

Show your work here: (7 points)

17. In the end, after you leased and then purchased the car, how much did you pay in total? Be sure to include the lease, Step 13, along with the purchase price from Step 16.

Total   cost of the car

\$

Show your work here: (5 points)

18. Would you consider leasing a car? Discuss the advantages and disadvantages of buying versus leasing a car.
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