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**Management 3 Quantitative Methods**

Quiz #6 Solution courtesy of Meena Tafazzoli

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The Problem A car dealer offers either 0% financing for 3 years or a $3,000 rebate on a $25,000 car. Assuming that you take the rebate (instead of the 0% financing) and can find a loan for 6% for 36 months, which deal gives you a smaller payment? 2

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**Pay 0% financing for 36 months**

My financing decision I want to buy a $25,000 car PLAN 1: Pay 0% financing for 36 months PLAN 2: Pay upfront with $3000 rebate, get a loan at 6% monthly payments (36 mos) =$25000/ 36 months = $ monthly payment [1 point] = $25,000 upfront less the $3,000 rebate as a downpayment = $22,000 loan Continued on next slide

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**Finding the monthly payments on the loan (PLAN 2)**

Recall… PV (loan) = PV (loan payments) 22,000 = Loan payments * PVFA (r/12,t*12) r= 6% annual interest rate compounded monthly! t = 3 years So …… r /12= 0.06/12= 0.005 [1 point] t *12mt= 3*12 = 36

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**The monthly payments on the loan (PLAN 2)**

22,000 = Loan payments * PVFA Let’s do the PVFA first PVFA(r/12, t*12) = [ (1- (1+r/12)^(-t*12) ] / r = ( ) / (.005) = / 0.005 =

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**The monthly payments on the loan (PLAN 2)**

22,000 = Loan payment * PVFA $22,000 = Loan payment * $22,000 / = Loan payment Loan payment = $669.28 [2 points]

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**Monthly loan payments for plan 2**

ON EXCEL Monthly loan payments for plan 2 = PMT (rate, nper, pv) = PMT (.005, 36, 22000) =$669.28

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