Final answer:
The monthly payment for a 5-year loan of $27,000 at 9.3% interest compounded monthly is approximately $558.21, which matches option A from the provided choices.
Step-by-step explanation:
The question asks for the monthly payment for a 5-year loan of $27,000 at 9.3% interest compounded monthly. To find the monthly payment, we can use the formula for the monthly payment on an installment loan, which is P = L[i(1+i)^n] / [(1+i)^n - 1], where P is the monthly payment, L is the loan amount, i is the monthly interest rate, and n is the number of payments (months).
In this case:
- L = $27,000
- i = 9.3% annual interest rate, which is 0.093 annually or 0.093/12 monthly
- n = 5 years * 12 months/year = 60 months
Let's calculate the monthly interest rate:
i = 9.3% / 12 = 0.00775 (monthly interest rate)
Now, let's calculate the number of payments:
n = 5 years * 12 months/year = 60 payments
Plugging the values into the formula:
P = 27000[0.00775(1+0.00775)^60] / [(1+0.00775)^60 - 1]
After calculations, we find that the monthly payment P is approximately $558.21, which corresponds with option A. Therefore, the monthly payment for this loan is $558.21.