Final answer:
The monthly payment for a 5-year car loan of $27,900 at 9.3% interest compounded monthly is approximately $597.52.
Step-by-step explanation:
To calculate the monthly payment of a $27,900 car loan over 5 years with a 9.3% interest rate compounded monthly, we must use the formula for the monthly payment of an installment loan, which is:PMT = P * [i*(1+i)^n] / [(1+i)^n - 1]where PMT is the monthly payment, P is the principal amount, i is the monthly interest rate, and n is the number of payments.Convert the annual interest rate to monthly by dividing by 12:i = 9.3% / 12 = 0.775%Convert the percentage to a decimal by dividing by 100:i = 0.775 / 100 = 0.00775The number of payments for a 5-year loan is:n = 5 years * 12 months/year = 60 monthsNow we plug the values into the formula:PMT = $27,900 * [0.00775 * (1+0.00775)^60] / [(1+0.00775)^60 - 1]
Calculate the numerator and the denominator separately and then divide:PMT ≈ $27,900 * [0.00775 * 1.565] / [1.565 - 1]PMT ≈ $27,900 * [0.0121] / [0.565]PMT ≈ $337.59 / 0.565PMT ≈ $597.5Therefore, the monthly payment for the car loan is approximately $597.52.To calculate the monthly payment for a 5 year car loan of $27,900 at 9.3% interest compounded monthly, we can use the formula for monthly loan payments:M = P * (r * (1+r)^n) / ((1+r)^n - 1)Where:M = Monthly paymentP = Principal amount (loan amountr = Monthly interest raten = Total number of payments (months)First, we need to calculate the values for r and n:r = 9.3% / 100 / 12 = 0.00775n = 5 years * 12 months/year = 60 monthsNow, we can plug these values into the formula:M = 27,900 * (0.00775 * (1+0.00775)^60) / ((1+0.00775)^60 - 1)After evaluating this expression, we find that the monthly payment for the car loan is approximately $555.36.