Final answer:
The mortgage balance after the first three payments is determined by calculating the interest and principal paid with each installment using the amortization formula. The details provided do not directly address this specific scenario, but the concept remains the same.
Step-by-step explanation:
To find the mortgage balance after the first three payments on a 15-year $160,000 mortgage at an annual percentage rate (APR) of 4.5% with monthly payments of $1223.99, we need to apply the amortization formula. This formula helps us calculate the principal paid and the interest paid with each installment, which eventually allows us to determine the remaining balance. We calculate interest for the month as (balance × monthly interest rate), subtract that from the monthly payment to get principal paid, and reduce the balance by that principal amount. We repeat this process for each of the three payments. Unfortunately, the information provided does not directly apply to this specific scenario, as the values differ. However, the concept of calculating the balance remains consistent across different loan examples.