19. Braeden wants to purchase a condo with a 25 -year mortgage of \( \$ 300000 \). The bank offers a mortgage an effective interest rate of \( 3.01 \% \) compounded monthly. What is Braeden's approximate monthly mortgage payment? How much interest will Braeden end up paying for his mortgage? Show your calculations.

To calculate Braeden's monthly mortgage payment, we can use the formula for a fixed-rate mortgage payment: \[ M = P \frac{r(1+r)^n}{(1+r)^n-1} \] Where: - \( M \) is the monthly payment - \( P \) is the loan principal (amount borrowed) - \( r \) is the monthly interest rate (annual rate divided by 12) - \( n \) is the number of payments (loan term in months) 1. **Determine the values**: - Principal \( P = 300,000 \) - Annual interest rate \( = 3.01\% \) or \( \frac{3.01}{100} \approx 0.0301 \) - Monthly interest rate \( r = \frac{0.0301}{12} \approx 0.0025083333 \) - Loan term in months \( n = 25 \times 12 = 300 \) 2. **Calculate the monthly payment \( M \)**: \[ M = 300000 \frac{0.0025083333(1+0.0025083333)^{300}}{(1+0.0025083333)^{300}-1} \] Calculating the values, it comes out to be approximately: \[ M \approx 1431.64 \] So, Braeden's approximate monthly mortgage payment is **$1431.64**. 3. **Calculate the total interest paid over the life of the loan**: - Total payments made over 25 years \( = M \times n = 1431.64 \times 300 \approx 429492 \) - Total interest paid \( = \text{Total payments} - P = 429492 - 300000 \approx 129492 \) Thus, Braeden will end up paying approximately **$129,492** in interest over the life of the mortgage.