Final answer:
The balance of a $200,000 mortgage at a 4% interest rate after one month is found by calculating the first month's interest, subtracting that from the monthly payment to find the principal paid, and then subtracting the principal from the original loan amount. This results in a balance of $199,454.71 after the first month.
Step-by-step explanation:
The question involves calculating the remaining balance of a mortgage after the first monthly payment. When you make monthly payments on a mortgage, part of the payment goes towards the interest, and part goes towards reducing the principal (the original loan amount). To find out the balance of the loan after the first month, we need to calculate the interest for the first month and subtract the principal portion of the first payment from the original mortgage amount.
To calculate the interest for the first month, we use the monthly interest rate (annual rate divided by 12) and multiply it by the original loan amount. The monthly interest rate for 4% annually would be 0.04/12, which is approximately 0.003333. Thus, the interest for the first month is 0.003333 * $200,000 = $666.67.
To calculate the principal paid, we subtract the interest for the first month from the total monthly payment. So the principal paid in the first payment is $1,211.96 - $666.67 = $545.29. Lastly, we subtract the principal paid from the original loan amount to find the remaining balance, which will be $200,000 - $545.29 = $199,454.71.