What will the balance be after the first month's payment on a $200,000 full amortized fixed-rate loan with a 5% rate and a monthly payment of $1,073.64?

To determine the loan balance after the first month's payment on a $200,000 full amortized fixed-rate loan at a 5% interest rate with a monthly payment of $1,073.64, we first need to understand how amortization works.

When you make a monthly payment on an amortized loan, part of that payment goes towards paying the interest on the loan for that month, while the remaining portion reduces the principal.

For this specific loan:

1. Calculate the monthly interest for the first month. The interest for the month is determined by multiplying the loan amount by the monthly interest rate. Since the annual interest is 5%, the monthly interest rate is 5% divided by 12, or approximately 0.41667%. Thus, the interest for the first month is calculated as follows:

   Interest = Principal x Monthly Interest Rate = $200,000 x 0.0041667 (5% / 12) = $833.33

2. Next, subtract the interest from the total monthly payment to find out how much of that payment is applied to the principal:

   Principal Reduction = Monthly Payment - Interest = $1,073.64 - $833.33