What will be the balance of the principal after the first month's payment on a fully amortized mortgage loan of $165,000 at an interest rate of 6.5%?

To determine the balance of the principal after the first month's payment on a fully amortized mortgage loan, we need to calculate the monthly payment and the amount of principal paid during that first month.

First, we find the monthly interest rate by dividing the annual interest rate by 12. For an interest rate of 6.5%, the monthly interest rate becomes 0.065 / 12, which is approximately 0.00541667.

Next, we calculate the monthly payment using the formula for a fully amortized loan:

[ M = P \frac{r(1 + r)^n}{(1 + r)^n - 1} ]

Where:

• (M) is the total monthly payment
• (P) is the loan principal ($165,000)
• (r) is the monthly interest rate (0.00541667)
• (n) is the number of payments (360 for a 30-year loan)

By substituting the values, we can calculate the monthly payment, which is approximately $1,051.43.

Now, we calculate the interest portion of the first month's payment. This is done by multiplying the principal by the monthly interest rate:

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