The 28/36 rule, solved from the payment back to the price

Published 2026-11-05 · Last reviewed 2026-11-06

Most calculators start with a price and produce a payment. Affordability runs the other way: it starts with a monthly budget set by two ratios and produces the largest price that fits. On $10,000 of gross monthly income with $2,000 of other monthly debts, the answer is a $1,600 housing budget and a maximum price of about $245,000. This guide is the algebra between those two numbers, because that is the part the page cannot show in one line.

Two ratios, and the smaller of the two budgets

The 28/36 rule is two budgets, and the housing budget is the smaller of them. The front-end ratio caps housing alone at 28% of gross monthly income - here $2,800. The back-end ratio caps every debt payment together at 36%, so the housing share of that ceiling is what is left after the car loan, the student loan and the minimum card payments: $3,600 - $2,000 = $1,600. The page reports which rule bound the answer, because $1,600 means something different when it comes from the 36% ceiling than when it comes from the 28% one.

Those two ratios are conventions rather than law: 28% and 36% are the conservative guidelines that US housing agencies have used for decades, while 31% and 43% are common maximums for conventional approvals. Both are inputs on the page, which is why a lender's own limits can be typed in instead of argued with.

Why the price cannot be read off a payment table

Property tax scales with the price, so the maximum cannot be read off a payment table: a house that costs more also costs more to own, before a single dollar of principal is repaid. With 1.1%tax and $2,100 of insurance a year, a $245,000 house carries $459.76 a month in tax, insurance and HOA dues - and that figure moves with the price the page is trying to solve for.

So the page solves it algebraically. Write the payment as principal and interest plus those fixed costs; note that principal and interest is the loan amount multiplied by a payment factor that depends only on the rate and the term; note that the loan amount is the price minus the down payment, and that the tax line is a percentage of the price. What is left is one linear equation in the price, and it has one solution: $1,600 of budget buys $1,140.24 of principal and interest, $224.76 of tax, $175.00 of insurance and $60.00 of dues - which is the budget exactly, and corresponds to a $185,000 loan plus the $60,000 down payment.

The result also has to be honest about what it leaves out. Mortgage insurance is not added to the payment the page solves for; it only flags that a down payment below 20% of this price makes PMI likely and that a lender may approve a smaller maximum. Closing costs, moving and repairs are not part of the DTI test at all. So the headline is the optimistic ceiling of the two ratios, not a number to spend up to.

Where these numbers come from

• Every figure above is calculated, not copied in. The budgets, the solved price, the loan amount and the monthly breakdown all come from one shared affordability calculation, which uses the same monthly-payment math as the mortgage pages. The calculator page and this guide run that same calculation, so they cannot print two different answers.
• Every release automatically checks the arithmetic: the front-end and back-end budgets, the line where the binding limit switches from one rule to the other, and the identity that the solved payment plus the other debts lands exactly on the DTI ceiling.
• The ratios are cited, not invented. The 28% front-end and 36% back-end limits follow the long-standing conventional lending guidelines used by US housing agencies. They are defaults on a page where both are editable, and the calculator says plainly that approval is a lender's decision on actual income, credit and down payment.

What this guide does not cover

It is not an approval, and it is not a budget: it deliberately leaves out maintenance, utilities, a longer commute and the savings one serious repair can consume. It does not model mortgage insurance in the payment, state-specific tax assessment rules, HOA special assessments, or the credit-score and cash-reserve conditions a lender actually underwrites. It also takes the income as given: a variable or self-employed income is averaged by the lender under rules this page does not apply. Treat the number as the most expensive house the two ratios allow, and then decide whether that is the house you want to be paying for.

Run your own numbers in the Home Affordability Calculator, price the payment precisely in the Mortgage Calculator, or work out the ratio on its own in the DTI Calculator.

Explanations and estimates only - not financial advice, and not a lending decision. Read the full disclaimer.