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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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  1. 10 November, 17:42
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    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
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