Question

A buyer of a 2003 Protege S Hatchback has a choice of 0% financing for 60 months or a $3,600 rebate. He plans to make no down payment. The buyer is able to qualify for 7% annual effective financing through his credit union and thereby take advantage of the rebate. Let Y denote his negotiated price for the Protege S Hatchback. How large must Y be in order for the 0% dealer financing to be preferable

Answer 1

To determine the value of Y for the 0% dealer financing to be preferable, we need to compare the total cost of financing with the rebate. If the negotiated price for the Protege S Hatchback is greater than $18,333, the 0% dealer financing would be preferable.

Step-by-step explanation:

To determine the value of Y for the 0% dealer financing to be preferable, we need to compare the total cost of financing with the rebate. Let's assume the negotiated price for the Protege S Hatchback is Y.

If the buyer chooses the 0% financing option, the total cost of financing would be 60 payments of (Y/60) per month.

If the buyer chooses the $3,600 rebate, they would have to finance the remaining amount (Y - $3,600).

Assuming the buyer qualifies for 7% financing through their credit union, the total cost of financing with the rebate would be 60 payments of (Y - $3,600) * (1.07/60) per month.

For the 0% dealer financing to be preferable, the total cost of financing with the rebate must be higher than the total cost of financing with the 0% option. So, we can set up the inequality:

60 * (Y/60) > 60 * (Y - $3,600) * (1.07/60)

Simplifying and solving for Y, we find that Y > $18,333. Therefore, if the negotiated price for the Protege S Hatchback is greater than $18,333, the 0% dealer financing would be preferable.

Answer 2

Answer: Option A which is the Dealership 0% financing option will be preferable if the Price of the car is less than the different of Loan monthly Payments minus Rebates.

Step-by-step explanation:

OPTION 1

A buyer pays 60 monthly instalments and the interest rate is 0%. This tells us that there is no interest the value of the debt (Which is the price of 2003 Protege S hatchback) will not increase over the period of 60%, with this option time value of money is not considered.

Option 2

The buyer receives a Rebate of $3600 if the car is paid for in cash. The buyer qualifies for a loan at an effective rate of 7% per annum. The amount of a loan will be the Price of a 2003 Protege S Hatchback. Assuming the Loan will also ave a period of 60 months, The Total amount Payable over the period of 60 months equals Loan Monthly payments multiplied by 60 months. The buyer receives a rebate of $3600, therefore The Net Amount Payable for Option 2 financing is found by multiplying Loan monthly payments by 60 months then subtract the Cash Rebate received of $3600

Let us now compare the two options to find out how Large must the Car be for option A to be preferable.

Y = The Price of a 2003 Protege Hatch Back, Which also equals the amount of debt over a period of 60 years (option A has no interest)

Monthly Payments of a loan = P

number of Periods = 60 months

Debt in 60 months versus Loan payments multiplied by 60 months - rebate

Therefore Y ∠ P x 60 months - $3600

Option A which is the Dealership 0% financing option will be preferable if the Price of the car is less than the different of Loan monthly Payments minus Rebates.