Loan Calculators
How to Calculate Mortgage Payments (Formula, Example, Calculator)
The amortisation formula behind every mortgage payment, worked through step by step, plus the taxes and insurance most calculators leave out.
By Sarah Mitchell · Reviewed by Legamoney Mortgage & Lending Desk
Key takeaways
- The payment formula is M = P × [ i(1+i)^n ] / [ (1+i)^n − 1 ], with i as the monthly rate and n as the number of months.
- Your actual bill is usually PITI: principal, interest, taxes, and insurance — often plus mortgage insurance and HOA dues.
- Early payments are mostly interest; the split flips gradually across the term.
- Term length changes the monthly payment far less than it changes total interest.
In this guide
The formula
Worked example
Borrow $320,000 over 30 years at 6.5% nominal. Then i = 0.065 / 12 = 0.0054167 and n = 360.
- (1 + i)^n = 1.0054167^360 ≈ 6.9919
- Numerator: i × 6.9919 = 0.0054167 × 6.9919 ≈ 0.037873
- Denominator: 6.9919 − 1 = 5.9919
- M = 320,000 × 0.037873 / 5.9919 ≈ $2,022.90 per month
What the first payment is made of
First three payments on the example loan
| Payment | Interest | Principal | Balance |
|---|---|---|---|
| 1 | $1,733.33 | $289.57 | $319,710.43 |
| 2 | $1,731.76 | $291.14 | $319,419.29 |
| 3 | $1,730.19 | $292.71 | $319,126.58 |
Interest for any month is simply the outstanding balance × i. Everything left over from the fixed payment reduces principal, which is why the principal share grows every month.
Run the numbers on your own figures
The parts most people forget: PITI
What lands on the monthly statement
| Component | Typical treatment | Included in the formula? |
|---|---|---|
| Principal and interest | Fixed on a fixed-rate loan | Yes |
| Property taxes | Escrowed monthly, reassessed periodically | No |
| Homeowners insurance | Escrowed monthly, renewed annually | No |
| Mortgage insurance (PMI/MIP) | Charged below a threshold of equity | No |
| HOA or condo dues | Billed separately or escrowed | No |
Levers that change the payment
- Rate: on the example loan, 0.5 percentage points is roughly $100 a month.
- Term: 15 years raises the payment but cuts total interest sharply.
- Deposit: a larger down payment cuts principal and can remove mortgage insurance.
- Extra payments: applied to principal, they shorten the term — see the mortgage extra payment calculator.
Sources
- 01Consumer Financial Protection Bureau — mortgage guidance and Ability-to-Repay rule
Federal consumer guidance on mortgages, disclosures, and lender underwriting obligations.
- 02Freddie Mac — Primary Mortgage Market Survey
Weekly national average mortgage rate survey, published every Thursday.
Frequently asked questions
What is the formula for a mortgage payment?
M = P × [ i(1+i)^n ] / [ (1+i)^n − 1 ], where P is the loan amount, i is the annual rate divided by 12, and n is the number of monthly payments. It returns principal and interest only.
How do I calculate mortgage interest for one month?
Multiply the current outstanding balance by the monthly rate. On a $320,000 balance at 6.5%, that is 320,000 × 0.0054167 ≈ $1,733.33 for the first month.
Why is my mortgage payment higher than the calculator says?
Most calculators return principal and interest. Escrowed property taxes, homeowners insurance, mortgage insurance, and HOA dues are added on top by the servicer.
Editorial transparency
- Written by
- Sarah Mitchell — Consumer credit writer — personal loans, debt and credit scores
- Reviewed by
- Legamoney Mortgage & Lending Desk — Editorial desk — mortgages, home equity, and consumer credit
- How this was researched
- The formula and worked example are standard amortisation arithmetic, reproduced in full so any figure here can be checked independently.
- 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
Sarah Mitchell covers borrowing outside the mortgage: personal loans, credit cards, student debt, debt payoff strategy and how credit scoring actually works. She uses CFPB guidance, the Federal Reserve's G.19 consumer credit release and the federal student aid rules as her reference points, and shows payoff arithmetic in full. She 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: Personal loans and loan comparison maths · Credit cards, interest accrual and payoff plans · Debt management and consolidation · Credit scores, reports and disputes
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Disclaimer
Figures here are arithmetic illustrations, not quotes. Confirm rates, escrow amounts, and fees with your lender. Consult a qualified professional before acting on any information here. Read our full disclaimer.
