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]
