Final answer:
To create an amortization schedule, calculate the monthly payment using the principal amount, the monthly interest rate derived from the APR, and the total number of payments. Then, generate the schedule by subtracting the monthly interest from the payment to find the principal reduction, and carry the reduced principal forward.
Step-by-step explanation:
To create the amortization schedule for a loan of $11,000 at an annual percentage rate (APR) of 9% paid monthly over three years, we follow these steps: First, we calculate the monthly interest rate, which is the APR divided by 12. In this case, the monthly interest rate is 9% / 12 months = 0.75% or 0.0075 as a decimal. Next, we need to determine the number of monthly payments, which over three years amounts to 3 years * 12 months/year = 36 payments.
Now, we use the formula for the monthly payment (M) of an amortized loan:
M = P * (i / (1 - (1 + i)^-n))
Where:
- P is the principal amount ($11,000)
- i is the monthly interest rate (0.0075)
- n is the total number of payments (36)
After performing the calculations, we find the monthly payment amount. Lastly, we generate the amortization schedule by subtracting the interest for the month from the monthly payment to find out how much of the payment goes towards reducing the principal, and then reducing the principal by this amount to carry forward for the next month.
Without providing specific numerical results, which requires a calculator or financial software, the above steps explain how you would generate the first three months of the amortization schedule.