How to Calculate a Mortgage Payment

Every mortgage payment is computed from one formula — the same one every lender and calculator uses. Understanding it demystifies how your payment works, why early payments are so interest-heavy, and how the rate and term shape what you pay. Here is the formula, a worked example you can do by hand, and the parts it leaves out.

The formula

The monthly payment M on a loan amount P, at annual interest rate r (as a decimal), over n months is:

M = P × [ r/12 × (1 + r/12)^n ] / [ (1 + r/12)^n − 1 ]

Where:

• P = loan amount (principal)
• r = annual interest rate as a decimal (6.5% = 0.065)
• r/12 = the monthly interest rate
• n = total number of payments (30 years = 360)

This is the standard amortization formula. It sets the payment so that, after n equal monthly payments, the loan balance is exactly zero.

A worked example

Take a $300,000 loan at 6.5% for 30 years. The inputs:

• P = 300,000
• r/12 = 0.065 ÷ 12 = 0.005417
• n = 360

Step one: compute (1 + 0.005417)^360. That is 1.005417 raised to the 360th power, which equals about 6.99. Step two, plug everything in:

M = 300,000 × [ 0.005417 × 6.99 ] / [ 6.99 − 1 ]

M = 300,000 × [ 0.03787 ] / [ 5.99 ]

M = 300,000 × 0.006322 ≈ $1,896

That $1,896 is the principal-and-interest payment. Over 360 payments, that is $682,600 total — of which $382,600 is interest, more than the $300,000 you borrowed.

Why the balance pays down so slowly at first

The formula explains the most confusing thing about mortgages: in the early years, your balance barely moves. In month one, the interest charge is 0.005417 × $300,000 = $1,625. Your $1,896 payment covers that interest plus just $271 of principal. It is not until the balance shrinks — years later — that the interest portion falls and the principal portion grows. This is why a $300,000 loan still owes over $270,000 after five years of payments.

What the formula leaves out

The formula computes principal and interest only. Your actual monthly payment is higher, because it adds:

• Property tax — collected monthly through escrow, varies by county.
• Homeowners insurance — also escrowed.
• PMI — if you put down less than 20%.

That is why a hand calculation of $1,896 understates the real bill, which might be $2,300 to $2,500 once tax and insurance are added. This full amount — the PITI — is what actually leaves your account each month.

How the rate and term change the payment

Two levers in the formula matter most. A higher rate raises M directly. A longer term (larger n) lowers M — but raises total interest dramatically, because you carry the balance longer:

The 15-year payment is about $717 higher, but it saves over $212,000 in interest. That trade-off — payment versus total cost — is the whole point of understanding the formula. See 15-year vs 30-year for the full comparison.

Skip the math

You do not need to compute this by hand. The HomeMath mortgage calculator runs the formula instantly and adds the taxes, insurance and PMI the formula ignores — so you see the true monthly payment, not just the loan math.