Final answer:
Using the present value of an annuity formula, Rick can afford a car priced at approximately $15,873.77. After rounding to the nearest hundred dollars, the closest answer given is $16,000.
Step-by-step explanation:
To calculate the maximum price of the car that Rick can afford, we will use the present value of an annuity formula, since the payments for the car are in the form of an annuity (a series of equal payments at regular intervals). The present value of an annuity formula is PV = PMT × ((1 - (1 + r)^{-n}) / r), where PV is the present value, PMT is the monthly payment, r is the monthly interest rate, and n is the total number of payments.
Given that Rick can afford payments of $300 per month, the annual interest rate is 7%, and the loan term is 5 years, we first convert the annual interest rate to a monthly rate by dividing by 12 (7% / 12 = 0.5833%), and then convert it to a decimal (0.5833% = 0.005833). The number of payments over 5 years is 5 years × 12 months/year = 60 payments.
Now we plug these numbers into the formula: PV = $300 × ((1 - (1 + 0.005833)^{-60}) / 0.005833). Using a calculator, we find that PV = $15,873.77. Rounding this to the nearest hundred gives us $15,900.
Therefore, the maximum car price Rick's budget can afford, when rounded to the nearest hundred dollars, is not precisely given in the options, but the closest is $16,000.