Liling wants to purchase a car. She secures an auto loan at 3.1% annual interest. Her budget allows her to pay about $280 a month over the next 4 years. What price car can she afford?

1. Convert the annual interest rate to a monthly interest rate:

i = \frac{0.031}{12} \approx 0.002583

2. Calculate the number of monthly payments:

n = 4 \times 12 = 48

3. Use the present value of an annuity formula:

PV = 280 \times \frac{1 - (1 + 0.002583)^{-48}}{0.002583}

4. Calculate the present value:

PV = 280 \times \frac{1 - (1.002583)^{-48}}{0.002583} \approx 12,624.81

Therefore, the maximum price of the car that Liling can afford is approximately **$12,624.81**.