Question

Stephen can afford $350 a month (excluding taxes and fees) for 6 yeats for a car loan. If the interest tate is 5.5 percent, how much can he afford to botrow to purchase a catr?

Answer 1

Stephen can afford to borrow approximately $18,042 to purchase a car with a monthly payment of $350 for 6 years at an interest rate of 5.5%.

Step-by-step explanation:

To determine the maximum loan amount that Stephen can afford, we can use the formula for the present value of an ordinary annuity:

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

Where PV is the present value or loan amount, PMT is the monthly payment, r is the interest rate per period, and n is the number of periods.

Using the given information, Stephen can afford to pay $350 a month for 6 years, which is a total of 72 months. The interest rate is 5.5% per year, so the monthly interest rate is 5.5% / 12 = 0.0046. Plugging these values into the formula, we can calculate the maximum loan amount that Stephen can afford:

PV = (350 / 0.0046) * (1 - (1 + 0.0046)^(-72))

Solving this equation, we find that Stephen can afford to borrow approximately $18,042 to purchase a car.