Rebate vs. Low APR. You managed to negotiate a price of $21,975 for a new car. To spur sales, the dealer is offering either a $1,500 rebate or dealer financing at 3.6% APR for 36 months. You can also get a 36-month auto loan from your credit union at 4.8% APR. Both loans require a $2,000 down payment. Decide whether you should use dealer financing or take the rebate and use bank financing.

 

1. First, figure out how much is your monthly payment with dealer financing. In other words, assume you make the down payment and finance the rest of the purchase using dealer financing. (Hint: Let c represent your monthly payment, PV = amount borrowed = purchase price - down payment, r = dealer financing APR / 12 = monthly rate and t = 36 = number of monthly payments. Then c = (PV x r) / (1- 1/(1+r)^t.)

Now we figure out how much is your monthly payment if you choose to use credit union financing instead. (Hint: The amount borrowed = price you negotiated minus the rebate and the down payment of $2,000. Use the same formula shown in Problem 1 with new values of PV and r to find c.)

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Buy vs. Lease. You managed to negotiate a price of $25,500 for a new car. If you choose to buy the car, you will make a $2,500 down payment and finance the rest of the purchase price with 48-month 5.4% APR loan from your bank. Alternatively, you can lease the car for by paying $1,500 down at $375 a month for 48 months. If you choose to buy the car at the end of the lease, it will require another payment of $11,000. Assuming you would like to keep the vehicle for longer than 48 months, is it cheaper to do so by buying or leasing the vehicle?

 

1. What is the present value of the monthly lease payments at the given APR? (Hint: Let PV = present value of the lease payments, c be the monthly lease payment, r = bank APR / 12 = monthly rate and t = 48 = number of monthly payments. Then PV = (c / r) x (1- 1/(1+r)^t ))
2. Next, find the present value the payment needed at the end of the lease to purchase the vehicle at the given APR. (Hint: Let FV = required payment to purchase vehicle at end of lease, r = bank APR / 12 = monthly rate and t = 48 = number of monthly payments. Then PV = FV / (1+r)^t )

What is the total present value of associated with the lease? (Hint: Sum the lease down payment due today and the present values of the monthly payments and the final payment found in Problems 3 and 4 above