Rasheed can afford a monthly car payment of $550 for 72 months at an annual interest rate of 7.5 percent.Which of the following is closest to the amount he will be able to borrow for a new car?
A)$3,984
B)$6,550
C)$31,810
D)$49,818

Question

Quizplus · Accepted Answer

The amount Rasheed can borrow can be calculated using the formula for the present value of an annuity because the car payment is an annuity (a series of equal payments at regular intervals). The formula is PV = P * [(1 - (1 + r)^-n) / r], where PV is the present value (amount he can borrow), P is the payment amount ($550), r is the monthly interest rate (7.5% annual rate divided by 12 months = 0.625% or 0.00625 as a decimal), and n is the total number of payments (72). Plugging in the values: PV = 550 * [(1 - (1 + 0.00625)^-72) / 0.00625], which gives a value close to $31,810. This calculation assumes the interest rate is compounded monthly, which is a common assumption for such calculations.

Rasheed Can Afford a Monthly Car Payment of $550 for 72