Mortgage Payment Formula

To calculate a fixed-rate mortgage payment, use the following formula:

M=P×r(1+r)n(1+r)n−1M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}M=P×(1+r)n−1r(1+r)n

Where:

• M = Monthly mortgage payment
• P = Principal loan amount
• r = Monthly interest rate (annual rate divided by 12)
• n = Total number of monthly payments (loan term in years multiplied by 12)

Step-by-Step Example

Assume the following:

• Loan amount (P): $300,000
• Annual interest rate: 6%
• Loan term: 30 years

1. Convert annual interest rate to monthly: r=6%12=0.005r = \frac{6\%}{12} = 0.005r=126%=0.005
2. Calculate the total number of payments: $$n=30\times 12=360$$
3. Apply the formula: M=300,000×0.005(1+0.005)360(1+0.005)360−1M = 300{,}000 \times \frac{0.005(1 + 0.005)^{360}}{(1 + 0.005)^{360} - 1}M=300,000×(1+0.005)360−10.005(1+0.005)360 After solving: $$M\approx 300,000\times 0.0059955\approx 1,798.65$$

So, the monthly mortgage payment is approximately $1,798.65, excluding property taxes, homeowners insurance, and mortgage insurance.

Additional Notes

• You can use an online mortgage calculator to simplify the process.
• Your total monthly payment may also include:
  • Property taxes
  • Homeowners insurance
  • Private Mortgage Insurance (PMI), if applicable
• Your actual interest rate may vary depending on credit score, loan type, and lender terms.