Mortgages
The Mortgage Payment Formula, Solved Step by Step (With a Worked Example)
M = P × r ÷ (1 − (1 + r)^−n), explained term by term and worked through on a $300,000 loan at 6.5% so you can reproduce a lender's quote yourself.
By Michael Bennett · Reviewed by Legamoney Mortgage & Lending Desk
Every fixed-rate mortgage payment in the world comes out of one equation. Once you can read each symbol, you can check any quote a lender sends you.
Key takeaways
- Every fixed-rate mortgage payment in the world comes out of one equation. Once you can read each symbol, you can check any quote a lender sends you.
- Reference example used throughout: $300,000 at 6.5% over 30 years — $1,896.20 a month.
- Every step below can be reproduced with a basic scientific calculator.
- Escrowed taxes and insurance are always calculated separately from principal and interest.
In this guide
- The method
- Point by point
- Write down the principal
- Divide the annual interest rate by 12 to get the monthly periodic rate
- Multiply the term in years by 12 to get the number of payments
- Compute (1 + monthly rate) raised to the negative number of payments
- Divide principal × monthly rate by 1 minus that result
- A short review checklist
- Questions worth asking
- Worked example
- Where people go wrong
- Check your answer
The method
- Write down the principal — the amount financed after your down payment, not the purchase price.
- Divide the annual interest rate by 12 to get the monthly periodic rate.
- Multiply the term in years by 12 to get the number of payments.
- Compute (1 + monthly rate) raised to the negative number of payments.
- Divide principal × monthly rate by 1 minus that result.
Point by point
Write down the principal
Write down the principal — the amount financed after your down payment, not the purchase price. This is the part most people skip, and it is where mortgage payment calculations costs money quietly rather than obviously.
Divide the annual interest rate by 12 to get the monthly periodic rate
Divide the annual interest rate by 12 to get the monthly periodic rate. Write the answer down before you act on it — an undocumented assumption here is impossible to audit later.
Multiply the term in years by 12 to get the number of payments
Multiply the term in years by 12 to get the number of payments. Check this against your own paperwork rather than a general guide, because the terms differ between providers.
Compute (1 + monthly rate) raised to the negative number of payments
Compute (1 + monthly rate) raised to the negative number of payments. If this changes, everything downstream of it changes too, so review it whenever your circumstances move.
Divide principal × monthly rate by 1 minus that result
Divide principal × monthly rate by 1 minus that result. Ask for this in writing. A verbal answer on mortgage payment calculations is not something you can rely on if it is later disputed.
A short review checklist
- Confirm which of the points above actually applies to your situation — several will not.
- Gather the documents that prove each figure you are relying on.
- Model the outcome with your own numbers before accepting anyone else's summary.
- Note the date you checked, because rules and rates on mortgage payment calculations change.
- Keep a copy of any written confirmation you receive.
Questions worth asking
- How does this apply to you: write down the principal — the amount financed after your down payment, not the purchase price?
- How does this apply to you: divide the annual interest rate by 12 to get the monthly periodic rate?
- How does this apply to you: multiply the term in years by 12 to get the number of payments?
- How does this apply to you: compute (1 + monthly rate) raised to the negative number of payments?
- How does this apply to you: divide principal × monthly rate by 1 minus that result?
Treat the list above as the agenda for a single sitting. Working through 5 specific questions with your own paperwork in front of you settles more about mortgage payment calculations than reading another general explanation, and it produces a written record you can revisit when something changes.
Worked example
First four payments on the reference loan
| Payment | Amount | Interest | Principal | Balance |
|---|---|---|---|---|
| 1 | $1,896.20 | $1,625.00 | $271.20 | $299,728.80 |
| 2 | $1,896.20 | $1,623.53 | $272.67 | $299,456.12 |
| 3 | $1,896.20 | $1,622.05 | $274.15 | $299,181.97 |
| 4 | $1,896.20 | $1,620.57 | $275.64 | $298,906.34 |
Where people go wrong
- Using the purchase price rather than the amount actually financed.
- Using the APR in place of the note rate, which overstates the payment.
- Rounding the monthly rate too early — keep six decimal places.
- Treating escrow as part of the loan calculation instead of a separate monthly deposit.
Check your answer
Build one month of the schedule. Interest is the balance multiplied by the monthly rate; the principal portion is whatever is left of the payment. If the closing balance matches a lender's schedule, your inputs are right.
Sources
- 01Consumer Financial Protection Bureau — Understanding loan options
Official explanation of fixed-rate amortisation and loan structures.
- 02Freddie Mac Primary Mortgage Market Survey
Weekly published average mortgage rates used to sanity-check rate scenarios.
Frequently asked questions
Do I need a financial calculator?
No. Any calculator with an exponent key handles the (1 + r)^−n term; a spreadsheet does it with the PMT function.
Why does my lender's quote differ slightly?
Usually because the quote includes escrow or mortgage insurance, or because the loan amount includes financed fees.
Does this work for personal and auto loans?
Yes — the same amortisation formula prices any fixed-rate instalment loan.
Editorial transparency
- Written by
- Michael Bennett — Mortgage writer — home financing, refinancing and interest rates
- Reviewed by
- Legamoney Mortgage & Lending Desk — Editorial desk — mortgages, home equity, and consumer credit
- How this was researched
- Worked with the standard published formula for this calculation and checked against the primary sources listed below.
- Corrections
- Spotted an error? Tell us and we will correct and re-date the page. See our editorial policy.
- Advertising disclosure
- Ad placements are clearly labelled and never influence editorial judgement or the ordering of comparisons.
About the author
Michael Bennett writes Legamoney's mortgage coverage: payment and amortisation maths, refinancing decisions, preapproval and underwriting, home equity and reverse mortgages. He works from HUD programme handbooks, CFPB rules under TILA and Regulation Z, and the FHFA conforming loan limits, and links to the weekly Freddie Mac survey rather than quoting a fixed rate. He works with the Legamoney Mortgage & Lending Desk.
How this article was checked
- Every factual claim is traced to a named regulator, government agency, or the provider's own published terms before publication.
- Figures that change — rates, limits, thresholds — link to the primary source that publishes them rather than being quoted as a fixed number.
- Worked examples are shown as full arithmetic so a reader can reproduce the result independently.
- Each guide is checked by the owning editorial desk before it is published, and again whenever the underlying rules change.
Covers: Mortgage payment and amortisation maths · Refinancing, break-even and closing costs · Preapproval, underwriting and affordability · Home equity, HELOCs and reverse mortgages
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Disclaimer
Figures on this page are worked examples produced with standard formulas and the assumptions stated. They are not an offer, a quote, or personalised financial advice. Consult a qualified professional before acting on any information here. Read our full disclaimer.