Final answer:
To determine the mortgage balance at the end of the 3-year term, we can calculate the monthly payment using the given information and then calculate the remaining balance after 36 payments. The correct mortgage balance is $114,600.42.The correct answer is option C.
Step-by-step explanation:
To find the mortgage balance at the end of the 3-year term, we need to calculate the monthly payment using the given information. The mortgage is $130,000 amortized over 15 years with an interest rate of 7.5% compounded semi-annually for the first 3 years. We can use the formula for calculating the monthly payment of an amortizing loan:
Monthly Payment = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where P is the principal amount, r is the monthly interest rate, and n is the total number of payments. Plugging in the values, we have:
Monthly Payment = $130,000 * (0.075 / 12) * (1 + (0.075 / 12))^(3 * 12) / ((1 + (0.075 / 12))^(3 * 12) - 1)
Solving this equation gives us a monthly payment of approximately $1,065.78.
Now, we can calculate the mortgage balance at the end of the 3-year term. We need to calculate the remaining balance after 36 monthly payments. Using the formula for the remaining balance of an amortizing loan:
Remaining Balance = P * ((1 + r)^n - (1 + r)^m) / ((1 + r)^n - 1)
Where P is the principal amount, r is the monthly interest rate, n is the total number of payments, and m is the number of payments made. Plugging in the values, we have:
Remaining Balance = $130,000 * ((1 + (0.075 / 12))^(15 * 12) - (1 + (0.075 / 12))^(3 * 12)) / ((1 + (0.075 / 12))^(15 * 12) - 1)
Solving this equation gives us a remaining balance of approximately $114,600.42.
Therefore, the correct option is C. $114,600.42.