Mortgage Payment Calculator
Understanding Your Mortgage Payment
A mortgage is a significant financial commitment, and understanding how your monthly payment is calculated is crucial for budgeting and financial planning. The primary components that determine your mortgage payment are the loan amount (principal), the annual interest rate, and the loan term.
The Mortgage Payment Formula
The standard formula for calculating a fixed-rate mortgage payment is:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
Where:
- M = Your total monthly mortgage payment
- P = The principal loan amount (the amount you borrow)
- i = Your monthly interest rate (annual rate divided by 12)
- n = The total number of payments over the loan's lifetime (loan term in years multiplied by 12)
Breaking Down the Components:
1. Principal (P):
This is the initial amount of money you borrow from the lender to purchase your home. It's the core amount that you'll need to repay.
2. Annual Interest Rate (i):
This is the percentage charged by the lender for borrowing the money. It's usually expressed as an annual rate. For the calculation, you need to convert this to a *monthly* interest rate by dividing the annual rate by 12 and then by 100 (to convert the percentage to a decimal).
For example, if your annual interest rate is 5%, the monthly interest rate (i) would be (5 / 12) / 100 = 0.00416667.
3. Loan Term (n):
This is the duration over which you agree to repay the loan. Common loan terms are 15 or 30 years. To get the total number of payments (n), you multiply the loan term in years by 12.
For a 30-year mortgage, n = 30 * 12 = 360 payments.
How the Calculator Works
Our mortgage payment calculator takes these three key inputs (Loan Amount, Annual Interest Rate, and Loan Term) and applies the formula above to provide you with your estimated monthly principal and interest payment. This calculation does NOT include other costs like property taxes, homeowner's insurance, or private mortgage insurance (PMI), which are often included in your total "escrow" payment.
Example Calculation:
Let's say you want to buy a home and take out a mortgage with the following terms:
- Loan Amount (P): $200,000
- Annual Interest Rate: 5%
- Loan Term: 30 years
First, we convert the annual interest rate to a monthly rate:
i = (5 / 100) / 12 = 0.05 / 12 = 0.00416667
Next, we calculate the total number of payments:
n = 30 years * 12 months/year = 360
Now, we plug these values into the formula:
M = 200000 [ 0.00416667(1 + 0.00416667)^360 ] / [ (1 + 0.00416667)^360 – 1]
M = 200000 [ 0.00416667 * (1.00416667)^360 ] / [ (1.00416667)^360 – 1]
M = 200000 [ 0.00416667 * 4.467744 ] / [ 4.467744 – 1]
M = 200000 [ 0.0186156 ] / [ 3.467744 ]
M = 200000 * 0.0053677
M ≈ $1,073.64
Therefore, the estimated monthly principal and interest payment for this mortgage would be approximately $1,073.64. Use our calculator above to find your personalized monthly payment!