Answer:
Hanna will pay a total of $481,144.20 in interest over the 35-year mortgage.
Step-by-step explanation:
Step 1: Calculate the monthly interest rate by dividing the APR by 12. =[tex]\(r = \frac{5.24\%}{12} = 0.00437\)\\[/tex]
Step 2: Calculate the number of monthly payments by multiplying the number of years by 12. = [tex]\(n = 35 \times 12 = 420\)[/tex]
Step 3: Calculate the monthly payment using the formula for monthly payments on a mortgage: [tex]\(M = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1}\)[/tex], where P is the principal (initial loan amount). = [tex]\(M = \frac{350000 \times 0.00437 \times (1 + 0.00437)^{420}}{(1 + 0.00437)^{420} - 1} \approx 1979.41\)[/tex]
Step 4: Calculate the total amount paid by multiplying the monthly payment by the number of monthly payments. = [tex]\(Total = M \times n = 1979.41 \times 420 \approx 831,144.20\)[/tex]
Step 5: Calculate the total interest paid by subtracting the principal from the total amount paid. = [tex]\(Interest = Total - P = 831,144.20 - 350,000 = 481,144.20\)[/tex] = The solution to the original problem is that Hanna will pay a total of $481,144.20 in interest over the 35-year mortgage.