a. She has negotiated a sales price of $46,585 and she has a $15,000 down payment. She is eligible for the full $10,000 cash rebate. Her bank has pre-approved her for a 72-month car loan at 3.24%. Assuming Elaine wants the cheapest overall price, which option should she take? Should she take the 0% financing offer for 66 months from the dealer, or should she borrow the money from her bank at 3.24% to pay off the dealer and receive the $10,000 cash rebate?

Question

Business

Gustavo Fletcher

10 November, 16:52

a. She has negotiated a sales price of $46,585 and she has a $15,000 down payment. She is eligible for the full $10,000 cash rebate. Her bank has pre-approved her for a 72-month car loan at 3.24%. Assuming Elaine wants the cheapest overall price, which option should she take? Should she take the 0% financing offer for 66 months from the dealer, or should she borrow the money from her bank at 3.24% to pay off the dealer and receive the $10,000 cash rebate?

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Answers (1)

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Julia Hess · Answer 1

Answer: Elaine should take Dealership's financing option.

Explanation:

Option A

Car Sale Price = $46 585

Down Payment = $15000

Interest rate = 0%

Period = 66 months

Value of Dealer Financing = $46585 - $15000 = $31585

Option 2.

Elaine takes the loan to pay for the car

R = 3.24%

Car price = Loan Amount = $46585

Period (n) = 72 months

Value of Option 2 Loan Financing = Loan Amount (1 + r) ^n

Value of Option 2 Loan Financing = $46585 (1 + 0.0324^/12) ^72

Value of Option 2 Loan Financing = $46585 (1 + 0.0027) ^72

Value of Option 2 Loan Financing = 56566.482756

Value of Option 2 Loan Financing = $56566.48

Elaine receives a Cash rebate of $10 000

Overall Value of option 2 = $56566.48 - $10 000 = $46566.48

Let us assume Elaine Pays the Down Payment of $15000 AND take A Loan to finance the rest of the Car amount

Car sale price = $46585 - $15000 = $31585

Loan Amount = $31585

Option 2 Loan Financing with down Payment

Option 2 Loan Financing = $31585 (1 + 0.0324^/12) ^72 + $15000

Option 2 Loan Financing = $31585 (1+0.0027) ^72 + $15000

Option 2 Loan Financing = 38352.524586 + $15000

Option 2 Loan Financing = $53352.524586

Elaine Receives a Cash Rebate of $10 000

Value of Option 2 with down payment = $53352.524586 - 10 000

Value of Option 2 with down payment = $43352.524586

Value of Option 2 with down payment = $43352.53

When Elaine pays a down payment and takes a loan of $31585, the overall finance is valued at $43352.53, When Elaine takes a loan for the entire car amount the Value of option 2 finance is $46566.48.

Dealership Option Financing Value is $31585. Elaine should take Dealership's financing option