Mortgage Calculator
Estimate your full monthly mortgage payment — principal, interest, and optional property tax, home insurance, PMI, and HOA — along with your loan amount, loan-to-value ratio, and the total interest you'll pay over the term. Everything runs in your browser.
Monthly payment
Example: $400,000 home, $80,000 down, 6.5% for 30 years ≈ $2,022.62 P&I.
Companion guide: How the monthly payment formula works derives the principal-and-interest formula this calculator runs — monthly compounding, the term in months, and what changes with rate and term — on a fictional loan. This page covers what the mortgage calculator adds on top of it: the loan amount, loan-to-value, and the tax, insurance, PMI, and HOA lines. Every explainer on the site is listed under Guides.
How your mortgage payment is built
A fixed-rate mortgage payment has a constant principal-and-interest amount for the whole term. In the worked example — a fictional $400,000 home with $80,000 down, which makes a $320,000 loan at 6.5% over 30 years — principal and interest come to $2,022.62 per month. Add $366.67 of monthly property tax (at an illustrative 1.1% of the home price per year) and $150.00 of insurance ($1,800 a year, spread across twelve months), and the total is $2,539.28. Over the full term the loan pays $408,142 in interest — about 1.3× the original loan amount, more than the principal all over again. Every figure on this page is computed when the page is built by the same tested engine that powers the calculator above; the rates and prices in the examples are illustrative inputs chosen for the arithmetic, not quotes.
What the engine computes, step by step
The form hands your inputs to one engine function, which validates them, runs the steps below in order, and returns a typed result — or an explicit, human-readable error if an input cannot be used. The interface only formats what comes back; it never does arithmetic of its own.
- Loan amount = home price − down payment. In Example A, $400,000 − $80,000 = $320,000. A down payment equal to or larger than the price is refused before any arithmetic runs, with the engine's own message: "The down payment must be less than the home price."
- Loan-to-value = loan ÷ price, shown as a percentage: 80% here, because 20% down leaves 80% of the price financed.
- Principal and interest use the standard amortized-loan (PMT) formula with monthly compounding, the convention behind US mortgages and most consumer loans: the annual rate ÷ 12 is the monthly rate, years × 12 is the number of payments (360 here), and the result is the one fixed payment that retires the balance exactly at the last month — $2,022.62 in the example. The companion guide derives it. One convention of the engine's is worth knowing: at an illustrative rate of 0% there is no interest to spread, so the principal is divided evenly across the term instead — $320,000 ÷ 360 months = $888.89 a month, with total interest of $0.
- Property tax per month = home price × the annual tax rate you enter ÷ 12. The tax line scales from the price, not from the loan.
- Home insurance per month = the annual premium you enter ÷ 12.
- PMI per month = loan × the annual PMI rate you enter ÷ 12, included only while the loan-to-value ratio exceeds 80%. At 80% LTV the line is $0.00 whatever rate is typed into the PMI field.
- HOA dues are added per month exactly as entered.
- Total = the sum of the lines above. The engine also runs the full month-by-month schedule on the loan to report the total interest and the total of payments.
| Line | How the engine computes it | Per month |
|---|---|---|
| Principal & interest | PMT on $320,000 at 6.5% over 360 months | $2,022.62 |
| Property tax | $400,000 × 1.1% ÷ 12 | $366.67 |
| Home insurance | $1,800 ÷ 12 | $150.00 |
| PMI | Not applied — LTV is 80% | $0.00 |
| HOA | None entered | $0.00 |
| Total | Sum of the lines above | $2,539.28 |
Month one, and why the interest share is so large
The schedule behind the total-interest line is computed one month at a time. Each month the engine charges interest on the balance still outstanding — balance × (annual rate ÷ 12) — and the remainder of the fixed payment reduces the principal. In month one of Example A the balance is the whole $320,000, so interest is $1,733.33 and only $289.28 of the $2,022.62 payment reaches principal: 85.7% of the first payment is interest. Across the first year the engine's schedule records $20,695 of interest against $3,577 of principal, leaving $316,423 owing at the end of year 1. By year 30 the split has inverted: $833 of interest against $23,438 of principal. Nothing is front-loaded by anyone; the balance is simply large for a long time, and the interest charge follows the balance.
Because the schedule is built month by month rather than from a closed-form total, the same engine reports exact payoff dates when extra principal is added. The Amortization Calculator shows the year-by-year rows for any inputs, and the Mortgage Payoff Calculator runs the with-and-without-extra comparison.
PITI and escrow
Lenders think in PITI: principal, interest, taxes, and insurance. The tax and insurance portions are often collected monthly into an escrow account and paid on your behalf when bills come due, so your out-of-pocket payment includes them even though they aren't part of the loan itself. PMI and HOA dues, where they apply, add to the monthly total too — which is why the "advanced" fields matter for a realistic number.
In the calculator the tax and insurance lines are plain divisions of the annual figures you enter — $366.67 and $150.00 in Example A — held constant for the whole term. Leaving an optional field blank sets that line to zero; the engine does not fill in an estimate of its own.
Down payment, LTV, and PMI
Your loan-to-value ratio is the loan divided by the home price. Put 20% down and LTV is 80%; put less down and it's higher, which usually triggers private mortgage insurance (PMI) until you build equity back to 20%. In the example, 20% down means an 80% LTV and no PMI. A smaller down payment lowers your upfront cost but raises both the loan and the monthly payment — and adds PMI. The Down Payment Calculator shows that trade-off directly.
Example B keeps the same fictional $400,000 house and 6.5% rate but puts $40,000 down instead, and enters an illustrative PMI rate of 0.5% of the loan per year plus $50 a month of HOA dues. The loan rises to $360,000 and LTV to 90%, and because that is above 80% the engine now applies the PMI line: $360,000 × 0.5% ÷ 12 = $150.00 a month. Principal and interest rise to $2,275.44 (a larger balance at the same rate and term); tax and insurance are unchanged because they scale from the price, not the loan; and the total comes to $2,992.11 — $452.83 a month more than Example A. Total interest over the term rises to $459,160.
Two things the PMI line is not. It is not a lifetime total: the engine reports PMI as a monthly amount at the starting loan-to-value ratio and does not compute the month in which PMI ends — PMI removal timing depends on your specific loan program, and PMI, Explained sets out the rules. And it is not partial: at or below 80% LTV the engine sets the line to zero regardless of the rate entered, which is why Example A shows $0.00 of PMI.
How the term changes the payment and the total interest
The term is the other input that reshapes the payment. Example C is Example A's loan — $320,000 at 6.5% — over 15 years instead of 30. The principal-and-interest payment rises to $2,787.54, $764.93 a month more, while total interest over the term falls from $408,142 to $181,758 — $226,385 less. The engine compares; whether a higher payment for fewer years fits a household's budget is not a question the arithmetic answers. The companion guide shows what changes with term and rate on a fictional loan.
The reference figure, recomputed
The methodology page names the figure the engine is validated against: a $200,000 loan at 6% over 30 years. Recomputed here when the page is built, the same engine returns a payment of $1,199.10 and total interest of $231,676, matching the figures the methodology page and the automated tests expect. That is the point of computing the copy rather than typing it: if the copy and the code ever disagreed, the site would fail to build rather than publish inconsistent numbers.
How to read the result
- The large "/ month" figure is the total of every line you entered — $2,539.28 in Example A.
- Principal & interest is the fixed PMT amount. It is the only line the rate and term affect.
- Property tax, Home insurance, PMI, and HOA appear only when they are greater than zero, so a result with no optional fields filled in shows principal and interest alone.
- Loan amount (…% LTV) is the loan and the loan-to-value ratio at the start of the loan. The ratio is not updated as the balance falls.
- Total interest over term is interest on the loan only, summed from the month-by-month schedule. It excludes tax, insurance, PMI, and HOA.
- Total of payments is the loan amount plus total interest — $728,142 in Example A — the sum of every principal-and-interest payment, not the full monthly total multiplied by the term.
Money is shown to the cent, or to whole dollars for large totals like lifetime interest; internally every calculation keeps the full precision of IEEE-754 double-precision arithmetic, and nothing is rounded between steps. Your lender's figure may differ by a few cents depending on their rounding and day-count conventions — the difference is presentational, not an error. The Copy result button places a one-line summary of the total, the principal and interest, and the loan amount on your clipboard.
Where the calculator stops
The limits are the engine's, and the methodology page states them. The calculators model fixed-rate, fully amortizing loans. They do not model adjustable-rate mortgages, interest-only periods, balloon payments, or negative amortization: whatever rate you enter is held fixed for every month of the term, and the Fixed vs. Adjustable Rate guide describes the structure this engine does not price. Property tax, insurance, PMI, and HOA are held constant for the whole term, so reassessments, premium changes, and the month PMI ends are outside the arithmetic. There are no closing-cost, points, or fee inputs — the Mortgage Points Calculator and the Refinance Break-Even Calculator handle those comparisons separately — and the engine does not know your lender's day-count or rounding conventions. Inputs are validated before any arithmetic runs: non-numeric, negative, infinite, or out-of-range values return a plain-language error instead of a number. And a correct calculation can still be the wrong calculation for your situation — choosing the right loan for a real-world decision is judgment we cannot automate.
Frequently asked questions
What does the monthly payment include?
Principal and interest (P&I) always, plus — if you fill in the optional fields — monthly property tax, homeowners insurance, PMI, and HOA dues. Lenders call the full figure PITI (principal, interest, taxes, insurance); many collect the tax and insurance portions in an escrow account.
How is the principal and interest calculated?
With the standard amortized-loan formula: the loan amount, monthly interest rate, and number of payments determine a fixed monthly payment that pays the loan to zero over the term. Early payments are mostly interest; later payments are mostly principal.
When do I have to pay PMI?
Private mortgage insurance is typically required when your down payment is under 20% — i.e. the loan-to-value ratio is above 80%. This calculator adds PMI only while LTV exceeds 80%. Once you build enough equity, PMI can usually be removed.
Does the calculator work out when PMI ends?
No. PMI is reported as a monthly amount at the starting loan-to-value ratio — $150.00 a month in Example B — and the engine does not compute the month in which it stops. PMI removal timing depends on your specific loan program; the rules are set out in the PMI, Explained guide on this site.
Why is so much of my early payment interest?
Interest is charged on the outstanding balance, which is highest at the start. As the balance falls, the interest portion shrinks and more of each fixed payment goes to principal — see the amortization schedule for the year-by-year split.
What does the "Total interest over term" line include?
Interest on the loan only, summed from the month-by-month schedule: $408,142 in Example A. It does not include property tax, insurance, PMI, or HOA, and the "Total of payments" line is the loan amount plus that interest — $728,142 — not the full monthly total multiplied by the term.
Are the property tax and insurance amounts exact?
They are estimates from the rates you enter. Real property tax varies by locality and reassessments; insurance depends on the property and coverage. Use your local tax rate and a real insurance quote for accuracy.
Why might my lender's payment differ from the calculator by a few cents?
Internally the engine keeps the full precision of IEEE-754 double-precision arithmetic and rounds only on screen, to the cent (or to whole dollars for large totals like lifetime interest). Your lender's figure may differ by a few cents depending on their rounding and day-count conventions — the difference is presentational, not an error.
Not financial advice: this calculator gives general educational estimates. Your real rate, taxes, insurance, PMI, and eligibility depend on your lender, location, and credit — confirm figures with a licensed mortgage professional before relying on them. Values are processed locally in your browser and never transmitted. See the methodology page.