Find the monthly payment needed to amortize principal and interest for the following fixed-rate mortgage. Mortgage amount: \( \$ 194,900 \) Term of mortgage: 5 years Interest rate: \( 8.5 \% \)

To calculate the monthly payment for a fixed-rate mortgage, we can use the formula for the monthly payment \( M \): \[ M = P \frac{r(1 + r)^n}{(1 + r)^n - 1} \] where: - \( M \) = monthly payment - \( P \) = principal (loan amount) - \( r \) = monthly interest rate (annual interest rate divided by 12) - \( n \) = total number of payments (loan term in months) Given: - \( P = 194,900 \) - Annual interest rate = \( 8.5\% = 0.085 \) - Monthly interest rate \( r = \frac{0.085}{12} \approx 0.00708333 \) - Term of mortgage = 5 years = \( 5 \times 12 = 60 \) months Now, we can substitute these values into the formula: 1. Calculate \( r \): \[ r = \frac{0.085}{12} \approx 0.00708333 \] 2. Calculate \( n \): \[ n = 5 \times 12 = 60 \] 3. Substitute \( P \), \( r \), and \( n \) into the formula: \[ M = 194900 \frac{0.00708333(1 + 0.00708333)^{60}}{(1 + 0.00708333)^{60} - 1} \] 4. Calculate \( (1 + r)^{n} \): \[ (1 + 0.00708333)^{60} \approx 1.48985 \] 5. Now substitute this back into the formula: \[ M = 194900 \frac{0.00708333 \times 1.48985}{1.48985 - 1} \] \[ M = 194900 \frac{0.0105501}{0.48985} \] \[ M = 194900 \times 0.02154 \approx 4195.77 \] 6. Finally, calculate \( M \): \[ M \approx 4195.77 \] Thus, the monthly payment needed to amortize the principal and interest for the mortgage is approximately **$4,195.77**.