# Management 3 Quantitative Methods

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Management 3 Quantitative Methods
Quiz #6 Solution courtesy of Meena Tafazzoli

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

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

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

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 =

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]

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