Final answer:
To find the new balance after the first mortgage payment, calculate the interest portion of the payment, subtract this from the total monthly payment to find the principal reduction, and then subtract that from the initial loan amount. The balance after the first payment of $663.67 on a $105,000 loan at 6.5% interest would be $104,905.08.
Step-by-step explanation:
To calculate the balance after the first payment on a $105,000 mortgage at a 6.5% annual interest rate with a monthly payment of $663.67,
we need to first determine how much of that payment is applied to interest and how much reduces the principal.
First, calculate monthly interest: ($105,000 x 0.065) / 12
= $568.75.
Then, subtract the monthly interest from the payment to see how much goes towards the principal: $663.67 - $568.75
= $94.92.
Finally, subtract the principal reduction from the initial loan amount to find the new balance: $105,000 - $94.92
= $104,905.08.
Therefore, after the first payment, the balance on the mortgage loan would be $104,905.08.