You are considering the purchase of new car. You have negotiated with the salesp

Question

You are considering the purchase of new car. You have negotiated with the salesperson at the dealership and you can purchase the vehicle for $30,000. You have $8,000 that you can use as a down payment.  

                       Prior to going into the dealership, you have set an absolute limit of $375 for the amount of monthly payments that you can make on the car. You are willing to finance over five years but you cannot exceed the payment of $375 per month. The dealer is willing to offer you financing at an annual rate of 6.5% for a 5-year loan. The dealer is willing to offer 5.5% financing on a 4-year loan.  

      1. Can you meet your payment restriction and finance the amount required for the car?  

    2. What is the maximum amount that you can borrow to meet your payment restriction if the loan is to be paid off in 5 years?  

    3. Suppose that you are limited to paying $375 per month but you want to pay the loan off in 4 years and not 5 years. What is the maximum amount that you can borrow?

Explanation / Answer

Equated Monthly Installments, EMI = Amount payable/PVA@ interest rate, for the loan period

1. Maximum payment permitted per annnum = $375 x 12 = $4500

EMI for 5 years loan = $22,000/PVAF@6.5%,5years = $22,000/4.156 = $5,293.55

EMI for 4 years loan = $22,000/PVAF@5.5%,4years = $22,000/3.505 = $6,276.75

No term loan can be availed within the restricted limit for financing the car.

2. EMI = Max amount/PVAF@6.5%,5years

$4500 = Max amount/4.156

Max amount = $18,702

3. EMI = Max amount/PVAF@5.5%,4years

$4500 = Max amount/3.505

Max amount = $15,772.5

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