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Charles and Cynthia are purchasing a house. They obtained a 30-year, [tex]$\$[/tex]535,000[tex]$ mortgage at an annual interest rate of $[/tex]3.6\%[tex]$ compounded monthly.

Calculate their monthly payment on the loan. Round your answer to the nearest cent.

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

Their monthly payment will be \$[/tex][tex]\(\square\)[/tex]

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Note: The formula provided in the original question was incorrect. The correct formula for the monthly payment [tex]\( M \)[/tex] on a mortgage is given by the corrected formula above, where [tex]\( P \)[/tex] is the loan principal, [tex]\( i \)[/tex] is the monthly interest rate, and [tex]\( n \)[/tex] is the number of monthly payments.

Sagot :

GinnyAnswer
To calculate the monthly payment on Charles and Cynthia's mortgage, let's follow these steps:

1. Identify the given data:
- Loan amount ([tex]\( P \)[/tex]) = [tex]$535,000 - Annual interest rate = 3.6% - Loan term = 30 years 2. Convert the annual interest rate to a monthly interest rate: - Annual interest rate = 3.6% - Monthly interest rate (\( r \)) = \(\frac{3.6\%}{12} = \frac{0.036}{12} = 0.003 \) (or 0.3%) 3. Calculate the total number of monthly payments: - Loan term = 30 years - Total payments (\( n \)) = 30 years × 12 months/year = 360 months 4. Use the formula to find the monthly payment \( M \): The formula is: \[ M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \] Plug in the values: \[ P = 535,000 \] \[ r = 0.003 \] \[ n = 360 \] 5. Calculate the numerator: \[ \text{Numerator} = P \cdot r \cdot (1 + r)^n \] \[ = 535,000 \cdot 0.003 \cdot (1 + 0.003)^{360} \] 6. Calculate the denominator: \[ \text{Denominator} = (1 + r)^n - 1 \] \[ = (1 + 0.003)^{360} - 1 \] 7. Divide the numerator by the denominator to get the monthly payment \( M \): \[ M = \frac{\text{Numerator}}{\text{Denominator}} \] 8. Round the result to the nearest cent: The calculated monthly payment \( M \) comes out to be approximately $[/tex]2432.35 when rounded to the nearest cent.

Therefore, their monthly payment will be:
[tex]\[ \boxed{2432.35} \][/tex]
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