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

2. 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

3. 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

4. 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

5. 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 =

6. 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]

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