Final answer:
The price of the car that can be afforded with a $55,000 car loan at 4.05% interest compounded monthly over 7 years equals approximately $59,433.12.
Step-by-step explanation:
To determine the price of the car that you can afford with a $55,000 car loan at 4.05% interest compounded monthly over 7 years, we should first calculate the total amount paid over the life of the loan. We're going to use the formula for the future value of an annuity because monthly payments into the loan are like an annuity that will add up to the total value of the loan at the end of the term.
The formula is: FV = P * [((1 + r)^nt - 1) / r], where P is the monthly payment, r is the monthly interest rate, n is the number of times the payment is made per year, and t is the number of years. However, for this situation, we reverse-engineer the formula to solve for P, since we know the future value (FV) of the loan, the annual interest rate, and the time frame.
We know that FV = $55,000, n = 12 (since the loan is compounded monthly), r = 4.05%/12, and t = 7 years. Plugging in these values:
FV = P * [((1 + 0.00405)^84 - 1) / 0.00405]
55000 = P * [((1 + 0.00405)^84 - 1) / 0.00405]
To find P, we can now solve the equation above. After doing the calculations, we determine that the monthly payment is approximately $708.48. Therefore, the car price you can afford is the total sum you would pay over the life of the loan, which is 7 years * 12 months/year * $708.48/month, which equals $59,433.12. Considering the given options, the closest option to the calculated price of the car would be option:
B) $58,129.42
However, please note that taxes, fees, and down payments might also affect the final amount you can allocate towards the vehicle's price. Be sure to include these in your budget when buying a vehicle. It's essential to think about how long you'll be paying off your auto loan, along with the impact this can have on your overall financial situation and affordability.
The closest option provided in the question that matches our calculation is option B) $58,129.42.