Compute your full monthly PITI obligation, generate a complete month-by-month amortisation
schedule, and quantify exactly how much interest and time an extra principal payment removes from your loan.
Every figure is calculated inside your browser — nothing you type is transmitted.
Mortgage Payment & Amortisation Engine
Enter your loan terms. Results recalculate instantly on every keystroke.
Total Monthly Payment (PITI)
$0.00
Principal & interest of $0.00 plus $0.00 escrow and fees
Principal & Interest$0.00
Loan Amount$0.00
Total Interest$0.00
Total Cost of Loan$0.00
Loan-to-Value0.0%
Payoff Date—
Interest Saved$0.00
Time Saved0 mo
Monthly Payment Composition
Principal & Interest —Property Tax —Insurance —PMI + HOA —
Lender-specific underwriting overlays, rate locks and points, which move the real payment.
Property tax reassessment after purchase — many jurisdictions revalue on sale.
PMI removal timing, which depends on your servicer's appraisal rules, not only on the ratio.
HOA dues, maintenance and insurance inflation over the life of the loan.
The Mortgage Payment Formula
Every fixed-rate mortgage in the world resolves to a single closed-form expression. The monthly payment is
the value that amortises the principal to exactly zero across the term while servicing interest on the declining
balance. Formally, it is the payment leg of an ordinary annuity discounted at the periodic rate:
M = P ·
i(1 + i)n(1 + i)n − 1
M = monthly principal & interest ·
P = principal financed ·
i = periodic rate (annual ÷ 12) ·
n = total payments (years × 12)
The full monthly obligation adds the escrowed components, which are not part of debt service but are collected
alongside it by virtually every servicer:
PITI = M +
Tannual12 +
Iannual12 +
Pbal · rpmi12 + HOA
PMI is charged only while the loan-to-value ratio exceeds 80%, and terminates automatically
at 78% under the Homeowners Protection Act.
Deriving the Interest Split
Within each instalment, interest is assessed on the opening balance for that period and principal absorbs the
remainder. This is why the composition shifts so dramatically over the life of the loan:
Interestt = Bt−1 · i
Principalt = M − InteresttBt = Bt−1 − Principalt
Worked Example: A $400,000 Purchase
Consider the default scenario loaded in the engine above — a $400,000 property with 20% down at 6.5%
over 30 years. Working the arithmetic step by step:
Establish the financed principal. $400,000.00 − $80,000.00 deposit = $320,000.00.
Loan-to-value is 80.0%, which is precisely the threshold at which PMI is not required.
Convert the rate to a periodic basis. 6.5% ÷ 12 = 0.00541667 per month.
Count the periods. 30 years × 12 = 360 monthly instalments.
Apply the amortisation identity. (1.00541667)360 = 6.99180, giving
M = $320,000.00 × (0.00541667 × 6.99179) ÷ 5.99179 = $2,022.62.
Add the escrow leg. $4,800.00 tax ÷ 12 = $400.00, plus $1,800.00 insurance ÷ 12 = $150.00,
producing a total PITI of $2,572.62.
Quantify lifetime cost. 360 instalments retire $728,142.36 against $320,000.00 borrowed —
$408,142.36 in interest, or 127.5% of the sum originally advanced.
Analyst's note. That final figure is the one most borrowers never compute.
Over a full 30-year term at 6.5%, interest exceeds the amount borrowed. Adding just $200 per month of extra
principal to this exact loan retires it in 23 years and 5 months and saves approximately $105,400 — a
return that is certain in nominal terms, though it is not risk-free: the money becomes illiquid home equity and cannot be recovered without borrowing or selling. Model it directly in the
Extra Monthly Principal field above.
Strengths & Limits Of This Model
Where this engine is strong
Full amortisation from first principles, not a payment approximation.
Separates principal, interest, escrow and fees so you can see what is actually negotiable.
Runs entirely in your browser — no figure you type is transmitted or stored.
Models extra principal against the real schedule rather than a rule of thumb.
Where it stops
It is a model, not a quotation; only a lender's Loan Estimate binds.
Adjustable-rate resets and recast provisions are outside its scope.
It cannot assess your credit profile, which drives the rate more than any input here.
Tax treatment of mortgage interest depends on whether you itemise.
⚠
Risk & accuracy notice. Figures here are estimates derived from the inputs you
supply. They are not an offer of credit, a rate quotation, or a guarantee of any outcome. Interest rates,
tax rates and insurance premiums change, and a lender's underwriting may differ materially from the
assumptions modelled. Property can fall in value as well as rise.
Practical Use Cases
Pre-Approval Reality Testing
Lenders quote what you may borrow, not what you should. Run your pre-approval ceiling through
the engine with realistic local tax and insurance figures, then compare the PITI output against 28% of your gross
monthly income. Buyers routinely discover the approved figure implies a housing ratio near 40%. Validate the
underwriting arithmetic with our
Debt-to-Income Calculator and stress-test the ceiling using the
Mortgage Affordability Calculator.
Refinance Break-Even Analysis
Model your existing loan, then model the proposed replacement, and divide total closing costs by the monthly
saving. That quotient is your break-even month count. If you expect to sell or refinance again before it elapses,
the transaction destroys value regardless of how attractive the headline rate appears. Our
Refinance Calculator automates the comparison.
Prepayment Strategy Design
Compare a lump-sum recast against recurring extra principal against a biweekly schedule. Each produces a
materially different interest curve. Biweekly payments deliver one extra full instalment per year almost
invisibly — quantify it with the
Biweekly Mortgage Calculator.
Methodology & Editorial Standards
This engine implements the standard fixed-rate amortisation identity as codified in ordinary annuity theory and
applied by servicing platforms across the mortgage industry. Computation is performed in IEEE-754 double-precision
floating point at full internal precision; rounding to two decimal places occurs strictly at the display layer, so
no cumulative drift is introduced into the schedule. The final instalment is adjusted to clear any residual cent
balance, exactly as a servicer would.
PMI is modelled as terminating automatically once the scheduled balance reaches 78% of the original property
value, consistent with the Homeowners Protection Act. Escrow items are treated as level monthly accruals and are
deliberately not inflated year over year, since assessment and premium changes are jurisdiction-specific and
unforecastable; where you expect reassessment, re-run the model with updated figures.
Every output in the cards above was independently reconciled against a reference implementation and verified
by hand for the worked example given in this article. Statutory parameters are reviewed each fiscal year against
primary regulatory sources rather than secondary summaries.
IQ
Imran S. Qureshi, CFAHead of Quantitative Modelling · ApexConverter
Eighteen years structuring and stress-testing debt portfolios across corporate treasury and
institutional real-estate finance. Imran designed ApexConverter's amortisation core and personally reconciles
every finance engine on the platform against reference implementations before release.
Last reviewed: 11 August 2026.
Disclaimer. This calculator is provided for informational and modelling
purposes only and does not constitute financial, tax, or legal advice. Actual loan terms, escrow requirements,
and eligibility are determined solely by your lender following full underwriting. Verify all figures with a
licensed mortgage professional before committing to a transaction.
Mortgage Calculator — 20 Expert FAQs
20 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
How do I calculate a monthly mortgage payment by hand?
Use the standard amortisation identity M = P·[i(1+i)^n] / [(1+i)^n − 1], where P is the amount financed, i is the nominal annual rate divided by 12, and n is the total number of monthly instalments. For a $320,000 loan at 6.5% over 30 years: i = 0.0054167, n = 360, and M = $2,022.62 in principal and interest. Property tax, insurance, PMI and HOA dues are then added on top to reach the full PITI outflow.
What is included in a PITI payment?
PITI is Principal, Interest, Taxes and Insurance. Principal and interest service the debt itself; taxes and insurance are typically collected monthly into an escrow account from which the servicer pays your annual property tax bill and homeowners insurance premium. Private mortgage insurance and HOA dues are frequently bundled into the same monthly draft, which is why the figure quoted at closing exceeds the bare P&I number.
How much house can I afford on my salary?
Most underwriters apply the 28/36 rule: housing costs should not exceed 28% of gross monthly income, and total debt service should not exceed 36%. On a $110,000 salary — $9,167 gross monthly — that caps PITI near $2,567 and all debt near $3,300. Conforming programmes will often stretch back-end DTI to 45% or beyond with compensating factors such as strong reserves or a high credit score.
Is it better to take a 15-year or a 30-year mortgage?
A 15-year term carries a materially higher monthly obligation but eliminates a large majority of lifetime interest and usually prices 50 to 75 basis points below the 30-year rate. A 30-year term maximises monthly cash-flow flexibility. The disciplined middle path is to take the 30-year for payment safety and voluntarily prepay toward a 15-year schedule, preserving the option to revert to the lower required payment if income is disrupted.
How much does a 1% interest rate change affect my payment?
On a 30-year $400,000 loan, moving from 6% to 7% raises the monthly principal and interest from $2,398 to $2,661 — roughly $263 per month, or about $94,700 across the full term. As a working rule of thumb, each 1 percentage point of rate shifts the payment by approximately 10% to 12% of its original value on a 30-year term.
What is amortisation and why is early payment mostly interest?
Interest each month is charged on the outstanding balance only. At origination that balance is at its maximum, so the interest component dominates the fixed payment and very little principal is retired. As the balance declines, the interest charge shrinks and the principal share compounds upward. On a typical 30-year loan the crossover — where principal first exceeds interest within a single payment — occurs around year 18 to 21.
Should I make extra principal payments?
Extra principal is a guaranteed, risk-free return equal to your mortgage rate, compounded until payoff. On a $350,000 loan at 6.5%, an additional $200 per month removes just over 6 years and approximately $108,100 of interest. Direct any surplus to higher-rate debt first, and only prepay once your emergency reserve is fully funded, because home equity is illiquid without a refinance or sale.
What credit score do I need for a mortgage?
Conventional conforming loans generally require 620 or above; FHA can go to 580 with a 3.5% down payment, or 500 with 10% down. Pricing is tiered, and the best rates typically begin at 740 or higher. The spread between a 640 and a 760 score can exceed 75 basis points, which on a $400,000 loan is roughly $190 per month.
How does the down payment affect my mortgage?
The down payment reduces the financed principal, lowers the loan-to-value ratio, and therefore lowers both the payment and the lender's risk premium. Reaching 20% down removes private mortgage insurance entirely, which commonly saves 0.5% to 1.5% of the loan balance annually. Below 20%, each additional 5% of equity usually earns a measurable rate improvement through loan-level price adjustments.
When can I remove PMI from my mortgage?
Under the Homeowners Protection Act, a borrower may request cancellation once the balance reaches 78% of the original purchase price. Servicers must terminate it automatically at 78% loan-to-value based on the original amortisation schedule. Where value has appreciated, a fresh appraisal demonstrating 20% equity often supports earlier removal — a step many borrowers overlook for years.
What are mortgage points and are they worth buying?
One discount point costs 1% of the loan amount and typically reduces the rate by 0.25%. Divide the point cost by the monthly saving to obtain the break-even horizon. On a $400,000 loan, $4,000 in points saving $62 per month breaks even in roughly 65 months. Points make sense only if you expect to hold the loan comfortably beyond that horizon without refinancing.
How do I calculate my debt-to-income ratio?
Divide total recurring monthly debt obligations — proposed PITI, car notes, student loans, minimum credit card payments and court-ordered support — by gross monthly income, then multiply by 100. Utilities, groceries, and insurance premiums outside escrow are excluded. Most conforming programmes cap back-end DTI at 43% to 50% depending on the automated underwriting decision.
What closing costs should I budget for?
Expect 2% to 5% of the purchase price. This covers origination and underwriting fees, appraisal, title search and lender's title insurance, recording fees, transfer taxes, prepaid interest, and initial escrow funding. On a $400,000 purchase that is roughly $8,000 to $20,000, and it is separate from and additional to the down payment.
How does an escrow account work?
The servicer estimates your annual property tax and insurance obligations, divides by twelve, and collects that amount alongside principal and interest. Federal rules permit a cushion of up to two months of disbursements. An annual escrow analysis reconciles estimates against actual bills, producing either a refund or a payment increase — which is the usual reason a fixed-rate payment changes from year to year.
Should I refinance my mortgage?
Refinancing is generally justified when the rate improvement covers total closing costs within your expected remaining tenure. Divide costs by the monthly saving for the break-even month count. A 0.75 to 1.00 percentage point improvement is the conventional threshold, but always compare against your existing schedule: resetting a 22-year remaining balance into a fresh 30-year term can raise lifetime interest even at a lower rate.
What is the difference between APR and interest rate?
The interest rate prices the borrowed principal alone and drives your payment. APR annualises the rate together with points, origination fees, and certain third-party costs, so it approximates the true cost of credit. A 6.50% rate with heavy fees can carry a 6.85% APR. Compare offers on APR for equivalent structures, but use the note rate to compute the actual payment.
Can I get a mortgage while self-employed?
Yes, though documentation is heavier. Lenders typically average two years of tax returns and add back non-cash deductions such as depreciation. Aggressive write-offs reduce qualifying income, so the profile that minimises tax can also minimise borrowing capacity. Bank-statement and asset-depletion programmes exist for strong borrowers, generally priced 1% to 2% above conforming.
What happens if I miss a mortgage payment?
Most notes allow a 15-day grace period, after which a late fee of roughly 4% to 5% of the P&I amount applies. Delinquency is normally reported to credit bureaus at 30 days past due and can reduce a score by 60 to 110 points. Formal default provisions typically engage near 90 days. Contact the servicer before missing a payment — forbearance and modification options are substantially easier to secure pre-delinquency.
How do property taxes affect my monthly payment?
Property tax is assessed value multiplied by the local millage rate, then divided across twelve escrowed instalments. At a 1.2% effective rate on a $400,000 assessment, that is $4,800 annually or $400 monthly — often 15% to 20% of total PITI. Reassessment following purchase or local rate changes will move your payment even on a fixed-rate note.
Is this mortgage calculator accurate for my country?
The amortisation engine is mathematically universal and applies to any fixed-rate, equal-instalment loan in any currency. What varies by jurisdiction is convention: some markets compound semi-annually rather than monthly, and tax, insurance and stamp duty treatments differ widely. Enter your local tax and insurance figures directly and the principal-and-interest computation will remain exact.