To calculate the monthly mortgage payment for a loan, you can use the formula for a fixed-rate mortgage payment, often referred to as the mortgage payment formula:
\[ M = P \frac{r(1 + r)^n}{(1 + r)^n - 1} \]
Where:
- \( M \) = monthly payment
- \( P \) = loan principal (amount borrowed)
- \( r \) = monthly interest rate (annual rate divided by 12)
- \( n \) = number of payments (loan term in months)
Given:
- Principal \( P = 265,351.00 \)
- Annual interest rate = 4.10% = 0.0410
- Monthly interest rate \( r = \frac{0.0410}{12} \)
- Loan term = 30 years \( = 30 \times 12 = 360 \) months
Steps to Solve:
-
Calculate the monthly interest rate \( r \): \[ r = \frac{0.0410}{12} \approx 0.00341667 \]
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Determine the total number of payments \( n \): \[ n = 30 \times 12 = 360 \]
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Substitute \( P \), \( r \), and \( n \) into the mortgage payment formula: \[ M = 265,351 \frac{0.00341667(1 + 0.00341667)^{360}}{(1 + 0.00341667)^{360} - 1} \]
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Calculate \( (1 + r)^n \): \[ (1 + 0.00341667)^{360} \approx 3.4406 \quad \text{ (using a calculator)} \]
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Substitute back to find \( M \): \[ M = 265,351 \frac{0.00341667 \times 3.4406}{3.4406 - 1} \] \[ M = 265,351 \frac{0.01175699}{2.4406} \approx 265,351 \times 0.00481 \approx 1,275.27 \]
So, the monthly mortgage payment is approximately $1,275.27.