Brad decides to purchase a \( \$ 235,000 \) house. He wants to finance the entire balance. He has received an APR of \( 4.2 \% \) for a 15 -year mortgage. What is Brad's monthly payment? Round your answer to the nearest hundredth. \( \begin{array}{l}\text { Regular Payment for Fixed } \\ \text { Installment Loans } \\ \text { Number of Fixed Payments } \\ \text { Required to Pay Off Credit Card } \\ \text { Debt }\end{array} \) Answer

To calculate Brad's monthly mortgage payment for the house he wants to purchase, we can use the formula for a fixed installment loan payment: \[ M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1} \] Where: - \( M \) is the monthly payment - \( P \) is the principal loan amount (the amount borrowed, which is \( \$235,000 \)) - \( r \) is the monthly interest rate (annual interest rate divided by 12 months) - \( n \) is the number of payments (loan term in months) Given: - The principal (\( P \)) = \( 235,000 \) - Annual interest rate (APR) = \( 4.2\% \) = \( 0.042 \) - Monthly interest rate (\( r \)) = \( \frac{0.042}{12} = 0.0035 \) - Term of the loan = \( 15 \) years = \( 15 \times 12 = 180 \) months (\( n = 180 \)) Now, plugging the values into the formula: \[ M = 235000 \times \frac{0.0035(1 + 0.0035)^{180}}{(1 + 0.0035)^{180} - 1} \] Calculating \( (1 + 0.0035)^{180} \approx 1.876 \), we can then compute: \[ M = 235000 \times \frac{0.0035 \times 1.876}{1.876 - 1} = 235000 \times \frac{0.006561}{0.876} \approx 235000 \times 0.007493 = 1755.27 \] Rounding to the nearest hundredth, Brad's monthly payment would be approximately \( \boxed{1755.27} \).