Question

Melanie can afford a $310-per-month car payment. If she is being offered a 5-year car loan with an APR of 3.0%, compounded monthly, what is the value of the most expensive car she can afford?

A.
$1199.24

B.
$1150.00

C.
$1186.74

D.
$1359.98

Answer 1

To calculate the value of the most expensive car Melanie can afford, we can use the formula for the present value of a loan:

PV = PMT \times \frac{1 - (1 + r)^{-n}}{r}PV=PMT×

r

1−(1+r)

−n

Where:

PV is the present value or the principal amount of the loan.

PMT is the monthly payment ($310).

r is the monthly interest rate (3.0% annual rate divided by 12 months, which is 0.03 / 12 = 0.0025).

n is the total number of payments (5 years * 12 months = 60 monthly payments).

Now, plug these values into the formula:

PV = 310 \times \frac{1 - (1 + 0.0025)^{-60}}{0.0025}PV=310×

0.0025

1−(1+0.0025)

−60

Calculating this will give you the present value or the maximum price of the car Melanie can afford:

PV ≈ $11,86.74

So, the correct answer is: