To calculate Charles and Cynthia's monthly mortgage payment, we'll use the fixed-rate mortgage formula. Given the parameters of their loan:
- Principal (P): [tex]$535,000
- Annual Interest Rate (r): 3.6% or 0.036
- Loan Term (n): 30 years
- Compounding Periods per Year: 12 (monthly)
Let’s break down the steps needed to find the monthly payment:
1. Calculate the monthly interest rate:
The monthly interest rate is the annual interest rate divided by 12 (monthly compounding):
\[
\text{Monthly Interest Rate} = \frac{0.036}{12} = 0.003
\]
2. Calculate the total number of payments:
The total number of payments over the life of the loan is the loan term in years multiplied by the number of compounding periods per year:
\[
\text{Total Payments} = 30 \times 12 = 360
\]
3. Use the fixed-rate mortgage formula to determine the monthly payment (M):
\[
M = \frac{P \times r \times (1+r)^n}{(1+r)^n - 1}
\]
Substituting the values we have:
\[
M = \frac{535,000 \times 0.003 \times (1 + 0.003)^{360}}{(1 + 0.003)^{360} - 1}
\]
4. Solve for M:
After calculating the values in the formula, the result is approximately:
\[
M = 2432.35
\]
Therefore, Charles and Cynthia’s monthly payment on the loan will be $[/tex]2432.35.
Thus, the monthly payment will be [tex]$\$[/tex]$ 2432.35
