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Charles and Cynthia are purchasing a house. They obtained a 30-year, [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.

The formula to calculate the monthly payment is:

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

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



Answer :

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

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