Let’s establish the known values first:
- Principal amount (loan amount): [tex]\( \$535,000 \)[/tex]
- Annual interest rate: [tex]\( 3.6\% \)[/tex] (0.036 as a decimal)
- Loan term: 30 years
To calculate the monthly payment, we can use the formula for the monthly mortgage payment:
[tex]\[ M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \][/tex]
where:
- [tex]\( M \)[/tex] is the monthly payment,
- [tex]\( P \)[/tex] is the principal loan amount (\[tex]$535,000),
- \( r \) is the monthly interest rate,
- \( n \) is the number of payments (monthly payments over the loan term).
First, calculate the monthly interest rate by dividing the annual interest rate by 12:
\[ r = \frac{0.036}{12} = 0.003 \]
Next, calculate the total number of payments over the loan term of 30 years:
\[ n = 30 \times 12 = 360 \]
Now, substitute the values into the formula:
\[ M = \frac{535,000 \times 0.003 \times (1 + 0.003)^{360}}{(1 + 0.003)^{360} - 1} \]
Simplify and solve the equation to find the monthly payment, which we'll denote as \( M \).
After performing the calculations, you will find that the monthly mortgage payment \( M \) is:
\[ M = \$[/tex]2432.35 \]
Therefore, the monthly payment on the loan will be \$2,432.35.
