Final answer:
To calculate the principal payment for the first month of a 10-year loan with monthly compounding and equal total payments, use the formula Principal payment = Total payment - Interest payment. The total payment can be calculated using the formula for the present value of an ordinary annuity. The interest payment for the first month can be calculated using the formula Interest payment = Loan amount × interest rate / number of periods. Substituting the given values into the formulas, the principal payment for the first month is $867.08.
Step-by-step explanation:
To calculate the principal payment for the first month, we need to use the formula:
Principal payment = Total payment - Interest payment
First, let's calculate the total payment. Since the loan has equal total payments, we can use the formula for the present value of an ordinary annuity:
Total payment = Loan amount / Present value factor
The present value factor can be calculated using the formula:
Present value factor = (1 - (1 + interest rate)^(-number of periods)) / interest rate
Substituting the given values into the formulas, we find that the total payment is $1,287.08. Now, let's calculate the interest payment for the first month:
Interest payment = Loan amount × interest rate / number of periods
Substituting the given values, we find that the interest payment for the first month is $420.00. Therefore, the principal payment for the first month would be:
Principal payment = $1,287.08 - $420.00 = $867.08