Mortgage Affordability Calculator

Purpose and model boundary

Use this calculator to find the highest price a household could pay for a home once two lender qualifying ratios, existing debt payments, available cash and the recurring costs of ownership are all counted. It reports the monthly housing budget those ratios allow, says which of the two is the one actually limiting you, and converts that budget into a purchase price.

Two points decide how the answer should be read. The budget covers the whole housing payment, not just the loan: principal, interest, property tax, homeowners insurance and any association dues come out of the same monthly figure, and only what remains after the fixed costs sizes a loan. And the price is solved rather than divided out. Property tax is entered as an annual share of the price, so the tax depends on the very price being looked for and the price appears on both sides of the payment equation. Sizing a loan from the budget first and adding tax afterwards gives a price that is too high, because the tax on that larger house no longer fits the budget.

The boundary is wide. This calculator does not decide approval: a lender also weighs credit history, cash reserves, employment, the property itself and its own internal overlays, none of which appear here. Mortgage insurance is not charged, although a deposit below one fifth of the price usually brings it and it is paid out of this same budget, so the real affordable price in that case is lower than the figure here. Closing costs are not deducted, even though they come out of the same cash as the deposit. Variable rates, buydowns and assistance programmes are not represented, and neither is tax reassessment after a sale, so the tax rate entered is assumed to be the rate that applies after the purchase. Income that is not gross, and gross income that is not steady, are outside the model entirely. The two ratios themselves are underwriting conventions rather than law, which is why they are editable inputs and not built-in constants.

Inputs and units

Association dues are the only optional input and ship blank, which is treated as no dues. Income and both ratios accept zero as an entered value but cannot be evaluated at zero, so a zero there returns a status rather than a price.

Governing relationships

Write income as I, other monthly debt payments as D, the front-end ratio as f and the back-end ratio as b. The housing allowance is I × f and the total-debt allowance after other debts is I × b − D. The binding budget is the smaller of the two, floored at zero:

budget = max(0, min(I × f, I × b − D)).

Insurance and dues are fixed monthly amounts that do not depend on the price, so they come out of the budget before any loan is sized. With annual insurance S and annual dues H, where blank dues read as zero, the amount left for loan and tax is

L = budget − S ÷ 12 − H ÷ 12.

The loan side uses the standard level-payment factor. With monthly rate r equal to the annual rate divided by twelve, and n equal to the term in years times twelve rounded to whole months, the payment per dollar borrowed is a = r ÷ (1 − (1 + r)^−n). That collapses to a = 1 ÷ n at a zero rate, and to a = 0 when there are no payments at all.

The payment equation sets the whole housing payment equal to the budget. With price P, deposit C and annual tax rate t:

L = a × (P − C) + t × P ÷ 12.

Price appears twice, so it is collected on one side and solved in closed form:

P = (L + a × C) ÷ (a + t ÷ 12).

Everything else follows. The loan is max(0, P − C), principal and interest is a × max(0, P − C), monthly property tax is P × t ÷ 12, the deposit share is C ÷ P and is reported as zero when P is zero, and headroom is the total-debt allowance less the binding budget. The fixed point is checked rather than assumed: principal and interest, property tax at the maximum price, insurance and dues add back to the binding budget, and an invariant inside the workbook asserts that in every state.

When L is zero or negative there is nothing to service a loan and the price falls back to the deposit itself. That is deliberate, because cash is still purchasing power even when no borrowing qualifies.

Calculation sequence

1. Check income, other debt payments, the interest rate, the term and the two ratios against the published input rules, in the order the status table below sets out.
2. Read association dues, treating a blank entry as zero.
3. Calculate the number of monthly payments as the term in years times twelve, rounded and floored at zero.
4. Calculate both allowances, take the smaller, and floor it at zero. That is the payment budget.
5. Record which allowance is the smaller, which is the binding ratio reported on the page.
6. Subtract monthly insurance and monthly dues to get the amount left for loan and tax.
7. Calculate the monthly rate and the payment factor per dollar borrowed, using the zero-rate branch when the rate is zero.
8. Solve the payment equation for the maximum price. If nothing is left for loan and tax, or the combined loan and tax factor is not positive, return the deposit as the price instead.
9. Derive the maximum loan, principal and interest at that price, monthly property tax at that price, the deposit share and the headroom.
10. Rebuild the budget from the price and confirm it reproduces the binding budget.
11. Recalculate the price across annual interest rates from 0% to 20% in half-point steps for the first chart, and split the monthly budget into its four parts for the second.
12. Evaluate the status conditions below in order; the first condition that is true is the one returned.

Outputs and interpretation

The three headline outputs are Maximum Price, Payment Budget and Binding Ratio, and they are meant to be read together. Maximum Price is the answer, Payment Budget is the monthly commitment that produces it, and Binding Ratio says which constraint you would have to relieve to move the answer. When the housing ratio binds, paying off a car does nothing for the price while more income or a larger deposit does. When the total-debt ratio binds, clearing another debt raises the price directly.

The first chart sweeps the annual interest rate from 0% to 20% in half-point steps and plots the maximum price against it, with your deposit drawn as a flat line underneath; where the curve meets that line, no borrowing qualifies and the price is the cash alone. The second splits the monthly budget into principal and interest, property tax, insurance and association dues, which shows how much of the allowance is spent before any loan is sized.

One useful sanity check: an extra dollar of deposit raises the maximum price by less than a dollar, because the slightly larger house carries slightly more property tax and that tax has to come out of the same budget. A price that rose by exactly the extra deposit would mean the tax scaling had been ignored. The gap closes as the property tax rate approaches zero, where an extra dollar of cash does buy exactly a dollar more house.

Validation and status logic

This calculator evaluates the status conditions in the order shown, from the top down. The first condition that is true is the one returned, and the final row is the fallthrough that applies when none of the earlier conditions holds. The names in the table are the intermediate quantities defined above: the housing budget that binds is the smaller of the two allowances, and the budget left for loan and tax is that figure after insurance and dues.

Order matters in a way that is easy to miss. A scenario can satisfy several conditions at once and only the first is reported. Very large other debt payments, for example, exhaust the whole allowance and also make the total-debt ratio the binding one, but the earlier and more serious status is the one returned. None of these statuses contains a substituted value; each is returned exactly as written above.

Assumptions and limitations

• Income, other debt payments, both ratios, the interest rate and all annual costs are held constant for the whole term. Nothing grows with inflation and nothing is indexed.
• Property tax is strictly proportional to purchase price at the rate entered, with no assessment ratio, exemption, cap or reassessment after sale.
• Insurance and dues are flat annual amounts divided by twelve. They do not scale with the price the model reaches, so at the extremes of the price range they are less realistic than in the middle.
• Mortgage insurance is not charged. Below roughly one fifth down it is usually required and comes out of this same budget, so the affordable price would be lower than reported. The Deposit Share output exists so this can be spotted.
• Closing costs are not deducted from the deposit, so the deposit entered should already be net of them.
• The loan is a fixed-rate level-payment mortgage. Adjustable rates, buydowns, points, interest-only periods, balloon structures and assistance programmes are not represented.
• The number of payments is rounded to whole months, so a fractional term is snapped to the nearest month before the payment factor is calculated.
• The two qualifying ratios are conventions lenders commonly quote, not rules. An underwriter may apply different ratios, count income differently, or decline a scenario this model reports as valid.
• The result is what two ratios allow. It is not a preapproval and says nothing about credit history, reserves, employment stability, the property itself or lender overlays.
• The rate sweep in the first chart varies only the interest rate. Every other input stays where you set it, including insurance and dues, which in practice move with the kind of house a different budget buys.

Restrictions and non-computing states

Income must be above zero, because both allowances are shares of it. Both qualifying ratios must be above zero and no greater than 100%. Other debt payments, the interest rate, the deposit, insurance and dues cannot be negative. The term must be at least one year, and the published input rules cap it at 40; an entry outside 1 through 40 years is rejected before any calculation runs. The property tax rate is accepted between 0 and 100%. Association dues are the one input that may be left empty, and a blank there means no association, which is the same arithmetic as zero.

Two non-computing states return figures rather than refusing. When other debt payments consume the whole total-debt allowance, the binding budget floors at zero and the maximum price falls back to the deposit, because cash on hand is still purchasing power even when no monthly payment qualifies. When insurance and dues alone exceed the housing budget, the same fallback applies for the same reason. Both are reported as CHECK states with the reason named, not as ordinary affordability estimates.

Errors and warnings

A rejected entry happens before any calculation. An input outside the published input rules, such as a term of 44 years or a negative deposit, is refused at the page and no figures are produced. Correct the entry and the calculation runs.

A NOT VALID or CHECK status is the model's own finding about inputs it accepted. NOT VALID means the combination does not describe an answerable question: no income, a negative rate or debt figure, a term under a year, or a qualifying ratio that is not a share between zero and one. Numbers shown beside a NOT VALID status are arithmetic residue, not an affordability estimate. CHECK means the arithmetic succeeded and the answer stands, with something worth noticing: the total-debt ratio binding rather than the housing ratio, or the fixed costs having taken the whole budget. These are findings, and repeating the calculation returns the same finding.

A connection or calculation-service failure is neither of those. It means the calculation service could not be reached or did not complete, so no answer exists for these inputs yet. It is a statement about availability, never a finding about your figures, and it is never reported as a zero, a blank result or an affordable price of nothing. Retry; if it keeps failing, the fault is on the platform side and not in what you entered.

The two qualifying ratios are debt-to-income measures. For the definition and a worked example, see the Consumer Financial Protection Bureau's explanation of what a debt-to-income ratio is, which states that the ratio is all monthly debt payments divided by gross monthly income. The specific figures of 28% for housing and 36% for housing plus other debt are conventions that lenders commonly quote rather than a published rule, which is why this calculator carries them as editable inputs and not as constants.

The composition of the monthly housing budget follows the Consumer Financial Protection Bureau's account of the costs that come with taking out a mortgage, which separates principal and interest from property tax, homeowners insurance and association dues. The Bureau's description of escrow and impound accounts explains why property tax and insurance are usually collected monthly alongside the loan payment, which is the reason this calculator charges them against the same monthly budget.

Mortgage insurance is the largest cost this calculator leaves out, and the Deposit Share output exists so that its absence is visible. The Consumer Financial Protection Bureau explains that private mortgage insurance may be required on a conventional loan with a down payment of less than 20% of the purchase price. Where that applies, the premium is paid out of the same budget modelled here, so the affordable price would be lower than this calculator reports.

Closing costs are not deducted from the deposit, which is why the deposit entered should already be net of them. The Consumer Financial Protection Bureau sets out the fees and charges paid at closing and who pays them. For broader context on the recurring obligations of ownership, including taxes, insurance, repairs and maintenance, see the Bureau's summary of the financial considerations of buying a home.

The level-payment mortgage factor and the closed-form solution for a price whose property tax scales with that price are standard financial mathematics. No outside source supplies them; they are derived and independently audited in the delivered workbook, whose method note and validation blocks record the derivation and the figures it was checked against.

These sources provide consumer context; they do not supply this calculator's assumptions and they do not certify its result. This calculator is informational and is not financial, mortgage, tax, investment or real-estate advice, and it is not a preapproval or a lending decision. It reports what two ratios allow, which is not the same as what a lender will approve. Results are highly sensitive to the interest rate, the qualifying ratios and the local property tax rate you enter.