Do all mortgages use this formula?

Fixed-rate, fully-amortizing loans do — the standard 15- and 30-year products. ARMs use the same formula per period but the rate (and therefore the payment) changes over time. Interest-only and balloon loans use modified versions.

Why does my exact payment differ by a few cents?

Lenders round each cent and adjust the final payment so the balance lands on $0. Different rounding policies produce small differences — usually under a dollar over the life of the loan.

Is APR the same as the interest rate?

No. APR includes upfront lender fees, so it's almost always slightly higher than the interest rate. Use APR when comparing offers, and the interest rate when computing the actual payment.

How to calculate a mortgage payment

A mortgage payment looks complicated, but the principal-and-interest piece is one formula. The rest — taxes, insurance, PMI, HOA — just adds on. This guide walks through each piece.

The principal & interest formula

Every fully-amortizing fixed-rate mortgage uses the same payment formula. The lender solves for a monthly amount that, paid for the loan's entire term, retires both the principal and all the interest exactly:

M = P * r * (1 + r)^n / ((1 + r)^n - 1)

P = loan amount (principal)
r = annual interest rate / 12  (monthly rate)
n = term in months  (e.g. 360 for 30 years)

When the rate is exactly 0%, the formula degenerates to M = P / n — no interest to charge, just principal divided evenly across all months.

A worked example

Take a $400,000 loan at 6.5% over 30 years.

P = 400,000
r = 0.065 / 12 = 0.005416666...
n = 360

(1 + r)^n  ≈ 7.0099
M ≈ 400,000 * 0.005416666 * 7.0099 / (7.0099 - 1)
M ≈ $2,528.27 per month

That's just principal & interest — the part the lender keeps. Almost nobody's real monthly payment is this small.

What gets added on top

Property taxes — typically 0.5%–2.5% of the home value annually, divided by 12 each month. Often escrowed by the lender.
Homeowners insurance — typically 0.25%–0.75% of home value annually. Also often escrowed.
PMI — private mortgage insurance, typically 0.3%–1.5% of the loan amount annually, charged when your loan-to-value is above 80%.
HOA dues — flat monthly amount specific to your community.

PITI = the realistic monthly cost

Add it all up: principal, interest, taxes, insurance, PMI, and HOA. That's your real monthly housing cost. Most lenders also use this number — not just principal & interest — when they evaluate affordability against your income.

Frequently asked

Do all mortgages use this formula?: Fixed-rate, fully-amortizing loans do — the standard 15- and 30-year products. ARMs use the same formula per period but the rate (and therefore the payment) changes over time. Interest-only and balloon loans use modified versions.
Why does my exact payment differ by a few cents?: Lenders round each cent and adjust the final payment so the balance lands on $0. Different rounding policies produce small differences — usually under a dollar over the life of the loan.
Is APR the same as the interest rate?: No. APR includes upfront lender fees, so it's almost always slightly higher than the interest rate. Use APR when comparing offers, and the interest rate when computing the actual payment.

Estimates only. This calculator is not a loan offer, loan approval, official Loan Estimate, Closing Disclosure, tax advice, legal advice, or financial advice. Actual payments, rates, taxes, insurance, mortgage insurance, closing costs, and loan terms may vary. Contact a qualified lender, tax professional, or financial advisor for guidance.