How affordability is estimated

The House Affordability Calculator takes six figures — gross annual income, monthly debt payments, a down payment, an interest rate, a loan term and an optional property-tax rate — and returns a maximum home price with four lines beneath it. This guide follows the arithmetic in the engine's order: two limits on the monthly housing budget, a payment factor that turns a monthly amount into a loan, and a rearrangement that lets property tax scale with a price not yet known. It is part of the guides collection; the methodology page states the conventions it rests on.

Every figure below is computed when this page is built, by the same engine that runs in your browser on the calculator page, from inputs invented for the example. None is a market figure; if the prose and the engine ever disagreed, the site would fail to build.

What the engine reads

The affordability function accepts annual income, monthly debts, a down payment, an annual rate and a term in years, plus three optional costs: a property-tax rate as a percent of the home's value per year, annual insurance and monthly HOA dues. The calculator form exposes the tax rate; the other two appear once below, in a labelled example. Income must be greater than zero, debts and the down payment may be zero but not negative, every dollar amount must be below the engine's cap — asked for more it answers "The annual income is larger than this tool supports." — and the rate and term must sit inside the engine's supported ranges; anything else comes back as an explicit error rather than a number.

The worked example throughout is a fictional household: $90,000 of gross annual income, $400 a month of existing debt payments, $30,000 saved for a down payment, a 6.25% rate, a 30-year term and a 1.2% property-tax rate. Entered into the calculator they return a maximum home price of $319,220; the rest of this guide shows where it comes from.

Step one: two limits on the monthly housing budget

The methodology page states the rule in one sentence: "Affordability uses the 28/36 debt-to-income guidelines, and property tax that scales with the home price is solved with a closed-form rearrangement rather than an approximation." The first half of that sentence is this step. The engine divides annual income by twelve to get gross monthly income — $7,500.00 in the example — and computes two ceilings from it.

• The front-end limit is the housing-cost share of gross monthly income. In the example it is $2,100.00, which is 28% of $7,500.00.
• The back-end limit is the total-debt share of gross monthly income — 36% here, or $2,700.00 — minus the monthly debts already being paid: $2,700.00 − $400 = $2,300.00.

The housing budget is the smaller of the two — $2,100.00, the front-end figure — and the engine records which one won as the limited by line. Nothing later in the calculation looks at income again.

Debts change which limit binds. Raise monthly debts to $900 with every other input unchanged: the front-end limit stays at $2,100.00, the back-end limit falls to $1,800.00, and the engine reports back-end. The price drops from $319,220 to $277,304, and from here each additional dollar of monthly debt takes exactly one dollar from the budget, because the subtraction happens before the comparison. At $600 of debts the two limits coincide at $2,100.00; the engine treats a tie as front-end.

Step two: the payment factor

A monthly budget has to become a loan amount. The engine uses the payment function the site's amortizing-loan calculators share — the standard amortized-loan (PMT) formula with monthly compounding, the annual rate divided by twelve over the term in months — and reads it in reverse: the payment factor is the monthly payment per dollar of principal at the chosen rate and term. At 6.25% over 30 years it comes to $6.16 per $1,000 borrowed, and dividing a monthly amount by it gives the loan that amount supports.

This is the only place the rate and term enter the calculation: a lower rate or a longer term makes each dollar a month carry more loan. The formula is the one the methodology page validates against its reference loan — $200,000 at 6% over 30 years, computed here as $1,199.10 a month — and the monthly payment formula guide takes it apart term by term.

Step three: the property-tax rearrangement

Without a tax rate the rest is one line: the price is the budget divided by the payment factor, plus the down payment. With a tax rate the calculation is circular. Monthly property tax in this engine is the home price times the annual rate, divided by twelve; it must fit inside the same budget as principal and interest; but the price is the thing being solved for. Rather than guess a price, compute its tax and repeat, the engine writes the budget as one equation and solves it exactly:

budget = (price − down payment) × payment factor + price × monthly tax rate
price = (budget + down payment × payment factor) ÷ (payment factor + monthly tax rate)

That second line is the "closed-form rearrangement" the methodology page refers to. In the example the monthly tax rate is 1.2% ÷ 12, the numerator is $2,100.00 + $30,000 × factor = $2,284.72, and the division returns $319,220.38 — the $319,220 the calculator displays once rounded to whole dollars. The loan is that price minus the down payment, $289,220; principal and interest on it, $1,780.78, plus monthly tax on the price, $319.22, add back to the $2,100.00 budget to the cent. The build re-checks that identity.

Leave the tax field blank and the tax term is zero. The same household then gets a price of $371,066 — $51,845 more — because the whole budget is being spent on principal and interest. A blank field reserves nothing for tax; it is not a statement that the tax is small.

Insurance and HOA dues, when supplied, are handled one step earlier: the annual insurance figure divided by twelve and the monthly dues come off the budget before the rearrangement runs, because neither scales with the price. With $1,500 a year of insurance and $150 a month of dues added to the example, $1,825.00 is left for principal, interest and tax, and the price comes down to $280,797; the four parts again sum to the $2,100.00 budget.

Reading the five result lines

The calculator prints the engine's result as five lines, each a quantity from the steps above:

• Maximum home price — the solved price, shown to the whole dollar: $319,220.
• Maximum loan amount — the price minus the down payment: $289,220. The engine floors this at zero rather than reporting a negative loan.
• Max monthly housing budget — the smaller of the two limits from step one: $2,100.00. It is reported before insurance and dues are subtracted.
• Principal & interest at that price — the loan times the payment factor: $1,780.78. The gap to the budget is the room reserved for tax and, when supplied, insurance and dues.
• Limited by — which limit set the budget: front-end in the example.

One reading note: the income field asks for gross income — before tax and deductions — because the two shares are shares of gross income; a take-home figure entered there yields a smaller budget.

What moves the number

Because the rate and term enter only through the payment factor, their effect can be tabulated. The grid holds every other input of the example fixed; the rates are fictional, chosen to bracket the example's 6.25%, and the terms are the three the calculator offers.

The down payment enters twice — in the numerator, converted into the monthly payment it would have carried, and in the loan line — so its effect depends on the tax rate. Raise the example's down payment from $30,000 to $60,000 and the price rises from $319,220 to $345,029: $0.86 of price per added dollar, because a dearer house carries more monthly tax inside the same budget. With the tax field blank the same change lifts the price from $371,066 to $401,066, exactly $1.00 per dollar.

Where the engine stops

The engine returns an error when the inputs leave nothing to solve for. A fictional household with $60,000 of income and $1,900 a month of debts has a back-end limit of −$100.00 — the debts exceed the total-debt share — and the calculator shows "Existing debts leave no room in the budget for a housing payment." Insurance and dues that outrun the budget produce "Insurance and HOA costs exceed the affordable housing budget." A term beyond the supported range answers "Terms are limited to 60 years."

The methodology page's limits apply here. The engine models fixed-rate, fully amortizing loans; it does not model adjustable-rate mortgages, interest-only periods, balloon payments or negative amortization. Property tax, insurance and HOA are "estimates from the rates and amounts you enter. Real figures vary by locality, reassessment, coverage, and lender." The affordability function has no PMI input, so nothing is reserved for mortgage insurance. And on the result itself the methodology page is explicit: "Affordability reflects general lender guidelines, not an underwriting decision. Actual approval depends on credit, employment history, the loan program, and lender-specific overlays." The number is the arithmetic of two shares, a payment factor and a tax term — nothing more is in it.

Frequently asked questions

A calculator, not advice: the calculator models the arithmetic; it does not know your lender's terms. The figures on this page are rounded views of full-precision values — your lender's figure may differ by a few cents depending on their rounding and day-count conventions, and the difference is presentational, not an error. For consequential financial decisions, verify results independently and consult a licensed mortgage professional. See the methodology page and the guides index.