You can afford monthly payments of $250, and you find a car dealer offering a 3.9% annual rate compounded monthly on a 5-year loan. Rounded to the nearest $100, what is the most expensive car you can afford?
A) $13,200
B) $13,600
C) $15,000
D) $15,600

Question

Quizplus · Accepted Answer

To find the most expensive car you can afford, you can use the formula for the present value of an annuity: $PV = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)$, where PV is the present value (the loan amount), PMT is the monthly payment ($250), r is the monthly interest rate (3.9% annual rate divided by 12 months = 0.325% or 0.00325 as a decimal), and n is the total number of payments (5 years x 12 months = 60 payments). Plugging in the values: $PV = 250 \times \left(\frac{1 - (1 + 0.00325)^{-60}}{0.00325}\right)$, which calculates to approximately $13,600.

You Can Afford Monthly Payments of $250, and You Find