The salesperson offers, "Buy this new car for $25,000 cash or, with an appropriate down payment, pay $500 per month for 48 months at 8% interest, compounded monthly." Calculate the "appropriate" down payment.

Question

Quizplus · Accepted Answer

We can use the formula for present value of an ordinary annuity to find the appropriate down payment:

PV = PMT x [(1 - (1 + r)^-n) / r]

Where PV is the present value of the loan, PMT is the monthly payment, r is the monthly interest rate (8%/12 = 0.00667), and n is the total number of payments (48). We can plug in the values given:

PV = 500 x [(1 - (1 + 0.00667)^-48) / 0.00667]
PV = 500 x (37.2892)
PV = $18,644.60

So the total cost of the car with financing would be $18,644.60 + the down payment. Setting this equal to the cash price of $25,000:

$25,000 = $18,644.60 + down payment
down payment = $6,355.40

Therefore, the appropriate down payment would be $6,355.40, and the best choice is B.

The Salesperson Offers, "Buy This New Car for $25,000 Cash