# intro to general math

**Question description**

**MATH125: Unit 3
Individual Project**

**Logic and Decision
Making**

**Does it make more
sense to buy or lease a car from a dealership?**

Being well-informed, 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 difference 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 principle value, *P*.

2.
Research available interest rates on this
particular car. This will be the rate, *r*.

3.
Decide how long you would like to take to pay off
this car. Choose between 3–7 years. This will be the time, *t*.

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

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

6. How much are your monthly payments?

7. Assume that you have 5% to put as a down payment. How much will you be putting down?

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

Now, consider the option to lease this same car.

9.
Most leases require a down payment. Assume that
the dealership is requiring a 5% down payment. What is the new value of *P* on your lease?

10. The appeal to a lease is a lower interest rate. Reduce the interest rate that you received on your purchase by 2%, with a minimum rate of 0.5%.

11. The length of a lease is typically 2–5 years. Choose how long you wish to lease this car.

12.
The monthly payment on a lease accounts for the
depreciation of the car’s value. Assume at the end of your lease, the car has
only retained 50% of its original value. What is your car’s value at the end of
the loan? Use this for your new value of *P*.

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

14. What is your total cost, in other words principle plus interest?

15. What are the monthly payments?

16.
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 12. 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?

17.
Instead of walking away, you could also purchase
the car for what it is now worth. Using *P*
from step 12, *r* from step *2* and *t* from step 3, calculate how much you would repay over the course
of this new loan.

18. How much did you pay in total for this car?

19. Would you consider leasing a car? Discuss the advantages and disadvantages for buying versus leasing a car.

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