Last updated: 2026-05-22

Maximum Home Price and the 28/36 Rule

Mortgage affordability is the maximum home price a buyer can finance while keeping housing costs within standard underwriting benchmarks. This calculator works backward from the 28/36 rule — the industry-standard debt-to-income guideline — to a maximum home price and loan amount, given gross income, existing monthly debt, and available down payment.

Lenders will pre-approve up to 43% — sometimes 50% — of gross income in total debt payments, because the loan is collateralized. That ceiling says nothing about whether the resulting payment leaves room for retirement contributions, childcare, maintenance costs, or a stretch of lower income. The 28/36 rule produces a more conservative, sustainable figure.

The 28/36 Rule

The 28/36 rule is the affordability guideline lenders and financial advisors have used for decades:

• Front-end ratio ≤ 28% — total monthly housing payment divided by gross monthly income.
• Back-end ratio ≤ 36% — all monthly debt payments (housing plus car, student, and credit-card minimums) divided by gross monthly income.

The monthly housing budget is whichever of these two produces the smaller payment. With little other debt, the 28% front-end ratio binds. With significant car or student loans, the 36% back-end ratio binds instead, because those payments draw on the same income.

FHA loans relax this to roughly 31/43, and qualified-mortgage rules permit up to 43–50% with compensating factors. Those higher limits secure approval; they do not make the payment comfortable.

Calculation Method

The monthly housing budget is the minimum of two constraints:

$\text{Budget} = \min\left(0.28 \cdot \text{Income}_{\text{mo}},\ \ 0.36 \cdot \text{Income}_{\text{mo}} - \text{Debts}\right)$

The monthly budget covers the whole housing payment — PITI: principal, interest, taxes, and insurance — plus any HOA dues. Property tax and homeowners insurance typically add 25–35% on top of principal and interest, so a calculation that ignores them overstates affordability.

The model subtracts estimated tax, insurance, and HOA from the budget, leaving the amount available for principal and interest, then inverts the amortization formula. For a monthly rate of $r_{\text{mo}} = r/12$ and a term of $n_{\text{mo}} = 12t$ months, the present-value factor turns a monthly payment into a loan balance:

$\text{Loan}_{\max} = \text{P\&I}_{\text{available}} \cdot \frac{1 - (1 + r/12)^{-12t}}{r/12}$

Because tax and insurance are themselves a percentage of the home price — which depends on the loan — the relationship is circular. The model solves it in closed form (one linear equation), so the result is exact rather than an approximation.

$\text{Home Price}_{\max} = \text{Loan}_{\max} + \text{Down Payment}$

A Worked Example

A household earning $90,000 with no other debt, $60,000 saved, looking at a 6.5% 30-year loan in an area with 0.9% property tax and 0.65% insurance:

• Gross monthly income: $7,500
• Housing budget (28%): $2,100/month
• After reserving ~$420 for tax and insurance, ~$1,680 supports principal and interest
• That inverts to a loan of about $266,000, for a maximum home price near $326,000

A lender might approve this same household for a $400,000+ loan. The gap is the lender's risk appetite, not the household's breathing room.

Levers That Raise the Maximum

Four factors move the maximum, in rough order of how sustainable they are:

1. A larger down payment — adds dollar-for-dollar to the home price, and past 20% it removes private mortgage insurance (PMI).
2. A lower interest rate — comparing multiple lenders, or buying points, can lower the rate when the buyer stays in the home long enough to recoup the cost.
3. Paying down other debt — retiring $100/month of car or card payments frees up back-end-ratio room.
4. A longer term — lowers the monthly payment, but raises total interest paid; it is the last lever to reach for.

Costs the Calculator Does Not Include

• PMI — applies on conventional loans with less than 20% down, adding 0.3–1.5% of the loan per year. A loan-to-value (LTV) ratio above 80% in the result means the affordability figure is slightly optimistic.
• Closing costs — typically 2–5% of the loan: origination, title, appraisal, escrow setup. These are budgeted separately from the down payment.
• Maintenance — roughly 1% of the home's value per year. On a $326,000 house that is about $3,300 annually that never appears on a loan disclosure.
• Credit and reserves — underwriters also weigh credit score, employment history, and cash reserves. A clean 28/36 result is necessary, not sufficient.

Using the Result

The figure represents a ceiling, not a target. Borrowing the full amount a lender offers leaves little margin for rate changes, repairs, or a stretch of lower income, so many buyers aim somewhat below the maximum. After settling on a target price, the Mortgage Payment Calculator layers on the full PITI breakdown, PMI, and an extra-payment path, showing the amortization curve for a specific loan.