How Mortgage Payments Are Calculated

The formula lenders actually use

Every fixed-rate mortgage in the world is paid off with the same piece of mathematics: the amortisation formula. If you borrow an amount P at a monthly rate r (the annual rate divided by 12) for n monthly payments, the payment is M = P × r × (1 + r)ⁿ ÷ ((1 + r)ⁿ − 1). That single line produces the payment on every 15-year and 30-year loan in every country.

Where do the inputs come from? The loan amount is the home price minus your down payment. The rate is the note rate your lender quotes — not the APR, which adds fees and is used for comparing offers, not for computing payments. And n is simply years × 12. Our [Mortgage Calculator](/calculators/mortgage.html) implements exactly this formula and shows the total interest alongside the monthly figure.

Where your money goes each month

The payment is constant for a fixed-rate loan, but its composition is not. In month one on a 30-year loan, interest is charged on the full balance, so most of your payment is interest. Every payment after that chips the balance down slightly, so the interest portion shrinks and the principal portion grows. This shift is slow: on a 30-year loan at 6.5%, it takes roughly 21 years before more than half of each payment goes to principal.

That asymmetry is why refinancing decisions and extra principal payments are most powerful early in the loan. An extra 100 toward principal in year 2 shortens the loan far more than the same 100 in year 25. It is also why the total-interest figure matters more than the payment figure when comparing terms: a 15-year loan costs more per month but a fraction of the lifetime interest. Model both with the [Loan / EMI Calculator](/calculators/loan.html) to see the difference in total cost.

What the payment estimate leaves out

Principal and interest are only the core of a real housing payment. On top of them come property taxes, homeowners insurance, and possibly HOA dues and mortgage insurance (PMI in the US when your down payment is under 20%). Depending on where you live, these extras commonly add 25–50% on top of the P&I figure — which is why our calculator displays the P&I number and explicitly labels it as excluding tax, insurance and HOA.

Closing costs are the other surprise. Budget 2–5% of the loan amount for origination, appraisal, title and legal fees, paid at completion. They do not change the monthly payment, but they change what you need on hand at purchase.

Rate, term, price: which lever moves what

Three inputs drive the payment, and they are not equally powerful. The rate compounds across the whole term: on a 280,000 loan over 30 years, dropping the rate from 6.5% to 6.0% saves about 55,000 in total interest — more than most people's annual salary. Term matters even more starkly: 15 years instead of 30 typically cuts total interest by more than half while raising the monthly payment by around 45%.

Price changes move payment and interest almost proportionally. Run three scenarios in the [Mortgage Calculator](/calculators/mortgage.html) — same price, three rates — and then a fourth with a shorter term. The [Interest Calculator](/calculators/interest.html) is useful alongside it for understanding the compounding mechanic underneath the amortisation.

A worked example

Price 350,000, down payment 70,000, rate 6.5%, term 30 years. Loan amount: 280,000. Monthly rate: 0.065 ÷ 12 ≈ 0.005417. n = 360. The formula gives ≈ 1,770 per month for principal and interest. Total payments over 30 years: about 637,000, of which roughly 357,000 is interest. Now the same loan over 15 years at 6.0%: payment ≈ 2,365, total interest ≈ 145,700 — less than half. Same house, same loan amount, radically different lifetime cost.

Frequently asked questions

**Does the formula change for variable rates?** The formula only describes fixed rates; variable loans reset periodically, so payments are recalculated at each reset. Estimate each phase with the current rate. **Can I include taxes in the payment?** Not in our calculator — add your local estimates separately. **Why is my first payment mostly interest?** Because interest is charged on the outstanding balance, which is at its maximum on day one. **Does paying bi-weekly help?** Yes — 26 half-payments equals 13 full payments a year, quietly shaving years off the term.