Questions: 1. The Mertzs have a 30-year mortgage on the purchase of their home. The mortgage on the loan was for 789,465, with a 6.33% APR for 30 years. (Do not round any numbers until your final answer. Round the final answer to the nearest cent.) (a) Find the monthly payment.

Solution Steps

To find the monthly payment for a mortgage, we can use the formula for the monthly payment of an amortizing loan. The formula is:

\[ M = P \frac{r(1+r)^n}{(1+r)^n - 1} \]

where:

• \( M \) is the monthly payment,
• \( P \) is the principal loan amount (\$789,465 in this case),
• \( r \) is the monthly interest rate (annual rate divided by 12),
• \( n \) is the total number of payments (loan term in years multiplied by 12).

We are given the following values for the mortgage calculation:

• Principal loan amount, \( P = 789465 \)
• Annual interest rate, \( \text{annual\_rate} = 6.33\% \)
• Loan term, \( \text{years} = 30 \)

To find the monthly interest rate, we convert the annual rate to a decimal and divide by 12: \[ r = \frac{6.33}{100} \div 12 = 0.005275 \]

The total number of monthly payments over 30 years is: \[ n = 30 \times 12 = 360 \]

Using the formula for the monthly payment \( M \): \[ M = P \frac{r(1+r)^n}{(1+r)^n - 1} \] Substituting the values: \[ M = 789465 \frac{0.005275(1 + 0.005275)^{360}}{(1 + 0.005275)^{360} - 1} \] Calculating this gives: \[ M \approx 4902.0224 \] Rounding to the nearest cent, we find: \[ M \approx 4902.02 \]

Final Answer