Calculate the monthly mortgage payment. Round to the nearest cent. \[ \$ 170,000 \text { is financed for } 30 \text { years at } 5 \% \text { APR } \]

To calculate the monthly mortgage payment, we can use the formula for a fixed-rate mortgage: \[ M = P \frac{r(1 + r)^n}{(1 + r)^n - 1} \] where: - \( M \) is the monthly payment, - \( P \) is the loan principal (amount financed), - \( r \) is the monthly interest rate (annual interest rate divided by 12), - \( n \) is the number of payments (loan term in months). Given: - \( P = 170,000 \) - Annual interest rate = 5% = 0.05 - Monthly interest rate \( r = \frac{0.05}{12} = \frac{0.05}{12} \approx 0.00416667 \) - Loan term = 30 years = \( 30 \times 12 = 360 \) months Now we can substitute these values into the formula: \[ M = 170000 \frac{0.00416667(1 + 0.00416667)^{360}}{(1 + 0.00416667)^{360} - 1} \] First, calculate \( (1 + r)^{n} \): \[ (1 + 0.00416667)^{360} \approx (1.00416667)^{360} \approx 4.467744 \] Now substitute this back into the formula: \[ M = 170000 \frac{0.00416667 \times 4.467744}{4.467744 - 1} \] Calculating the numerator: \[ 0.00416667 \times 4.467744 \approx 0.018598 \] Calculating the denominator: \[ 4.467744 - 1 \approx 3.467744 \] Now substitute these values into the formula: \[ M = 170000 \frac{0.018598}{3.467744} \approx 170000 \times 0.005366 \] Calculating the final monthly payment: \[ M \approx 170000 \times 0.005366 \approx 911.22 \] Thus, the monthly mortgage payment is approximately: \[ \boxed{911.22} \]