The salesperson offers,"Buy this new car for $25,000 cash or,with appropriate down payment,pay $500 per month for 48 months at 8% interest." Assuming that the salesperson does not offer a free lunch,calculate the "appropriate" down payment.

Question

Quizplus · Accepted Answer

We can use the formula for the present value of an annuity to solve this problem.

$25,000 is the present value of a lump sum payment, so we don't need to calculate anything for that option.

For the financing option, we need to find the present value of the future payments (48 payments of $500 each) at 8% interest.

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

Where: 
PMT = $500 
r = 8% 
n = 12 (since the payments are monthly) 
t = 4 (4 years = 48 months)

Plugging in the values, we get:

PV = $500 x (1 - (1 + 0.08/12)^(-12x4)) / (0.08/12) 
PV = $20,479.36

So, the appropriate down payment would be:

Down Payment = $25,000 - $20,479.36 
Down Payment = $4,520.64

Therefore, the best choice is B, with an appropriate down payment of $4,520.64.

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