Finance · Debt Amortisation

Mortgage Calculator

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.

Loan Structure
$
$
20.0%
%
6.50%
Escrow & Recurring Costs
$
$
$
%
$
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

Balance & Cumulative Interest Over Time

Remaining Balance Cumulative Interest Equity Accrued

Annual amortisation summary
YearPrincipal PaidInterest Paid Total PaidEnding Balance

What this result does not account for

  • 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 − Interestt     Bt = 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:

  1. 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.
  2. Convert the rate to a periodic basis. 6.5% ÷ 12 = 0.00541667 per month.
  3. Count the periods. 30 years × 12 = 360 monthly instalments.
  4. Apply the amortisation identity. (1.00541667)360 = 6.99180, giving M = $320,000.00 × (0.00541667 × 6.99179) ÷ 5.99179 = $2,022.62.
  5. 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.
  6. 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.

Imran S. Qureshi, CFA Head 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.

Related Finance & Mortgage Engines