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How to Calculate Mortgage Payments
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)nWhere:
- 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)
Assume the following:
- Loan amount (P): $300,000
- Annual interest rate: 6%
- Loan term: 30 years
- Convert annual interest rate to monthly: r=6%12=0.005r = \frac{6\%}{12} = 0.005r=126%=0.005
- Calculate the total number of payments: n=30×12=360n = 30 \times 12 = 360n=30×12=360
- 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≈300,000×0.0059955≈1,798.65M \approx 300{,}000 \times 0.0059955 \approx 1,798.65M≈300,000×0.0059955≈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.
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