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

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.

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.

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