Mortgage Payment Calculator
Understanding Your Mortgage Payment
A mortgage payment is the amount you pay each month to your lender to repay the loan used to purchase your home. This monthly payment typically includes several components, but the most significant ones are the principal and interest (P&I). The calculation determines how much of your payment goes towards paying down the loan balance (principal) and how much is paid as interest to the lender.
How the Mortgage Payment is Calculated
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 (Principal & Interest)
- P = The principal loan amount (the amount you borrow)
- i = Your monthly interest rate (your annual interest rate divided by 12)
- n = The total number of payments over the loan's lifetime (your loan term in years multiplied by 12)
Example Calculation
Let's consider an example:
- Loan Amount (P): $300,000
- Annual Interest Rate: 4.5%
- Loan Term: 30 Years
First, we need to find the monthly interest rate (i) and the total number of payments (n):
- Monthly Interest Rate (i) = 4.5% / 12 = 0.045 / 12 = 0.00375
- Total Number of Payments (n) = 30 years * 12 months/year = 360
Now, plug these values into the formula:
M = 300000 [ 0.00375(1 + 0.00375)^360 ] / [ (1 + 0.00375)^360 – 1]
M = 300000 [ 0.00375(1.00375)^360 ] / [ (1.00375)^360 – 1]
M = 300000 [ 0.00375 * 3.73395 ] / [ 3.73395 – 1]
M = 300000 [ 0.013999 ] / [ 2.73395 ]
M = 4199.70 / 2.73395
M ≈ $1,536.15
So, the estimated monthly principal and interest payment for this mortgage would be approximately $1,536.15. Remember that this calculation often excludes other costs like property taxes, homeowners insurance, and potentially Private Mortgage Insurance (PMI), which would increase your total monthly housing expense.