Every house hunt starts with the wrong number: the biggest mortgage a lender will approve. That number is the maximum the bank is comfortable risking — not the price you can live with month after month. The distance between those two numbers is where first-time buyers get into trouble, and it comes down to two ratios and four forgotten costs. Here is the five-step math behind the lender’s 28/36 rule, worked out with real numbers, so you can set your own ceiling before you ever talk to a bank.
The 28/36 rule, in plain English
DTI — debt-to-income — is the share of your gross monthly income already promised to debts. Lenders draw two lines in it. The front-end ratio caps your housing payment at about 28% of gross monthly income. The back-end ratio caps all of your monthly debts, mortgage included, at about 36%. The lower of the two prices wins.
What counts as a debt: car payments, student loans, credit-card minimums, child support, and alimony. What does not: groceries, utilities, subscriptions, and income taxes — lenders ignore them entirely. The ratios come from decades of default data: past a 36% back-end ratio, missed payments climb fast, which is why the number sticks.
Step-by-step: the affordability math
- Monthly income. Divide gross annual income by 12. Use base salary — bonuses and overtime are averaged over two years by lenders and discounted, so plan without them.
- Your two budgets. Front-end budget = 28% × monthly income. Back-end budget = 36% × monthly income − your other monthly debts.
- The payment factor K. Each dollar of house price costs K dollars per month: (1 − down payment) × R for principal and interest, plus (property tax rate + insurance rate) ÷ 12, plus estimated PMI when the down payment is under 20%. R is the amortization factor: r ÷ (1 − (1 + r)^−n).
- Two prices, keep the lower. Price = (budget − HOA) ÷ K, computed for each budget. That is your ceiling.
- Sanity checks. Down payment = down % × price — can you actually write that check? And does the monthly payment leave room for utilities, maintenance, and saving?
Worked example: a $100,000 salary
$100,000 income, $500/mo in other debts, 20% down, 6.75% APR on a 30-year loan, 1.1% property tax, 0.3% insurance, no HOA.
1. Monthly income: $100,000 ÷ 12 = $8,333.
2. Two budgets: 28% × $8,333 = $2,333/mo for housing; 36% × $8,333 − $500 = $2,500/mo for everything.
3. Payment factor: K = 0.8 × 0.006486 + 0.014 ÷ 12 ≈ 0.00636 — each $1,000 of price costs about $6.36/mo.
4. Two prices: $2,333 ÷ 0.00636 ≈ $367,100; $2,500 ÷ 0.00636 ≈ $393,400. The 28% rule binds.
5. The check: loan $293,680 → P&I $1,905 + tax $337 + insurance $92 = $2,333/mo, with a $73,420 down payment.
The four costs that shrink your budget
Property tax. The silent budget-eater: around 1.1% of the price per year nationally, but it swings wildly — roughly 1.8% in Texas, over 2.4% in New Jersey. On a $367,100 home that is the difference between $337/mo and $735/mo.
Homeowners insurance. Usually 0.2–0.4% of the price per year — about $92/mo in the example. Coastal and wildfire zones run higher.
HOA dues. Flat monthly fees, $0 to $500+, that come straight off your housing budget before the price is even computed.
PMI. Under 20% down, private mortgage insurance adds about 0.5% of the loan per year — roughly $119/mo on the example at 10% down. It drops off at 20% equity on conventional loans, which is one more reason the down payment matters.
Three ways to raise your ceiling
1. Grow the down payment. More down means a smaller loan, no PMI at 20%, and a lower K — every lever points the same way. This is the single biggest move most buyers can make.
2. Pay down other debts. Every $100/mo of debt you eliminate buys roughly $15,700 more house at 6.75% rates, because it flows straight into the back-end budget. A paid-off car can be worth more house than a bigger down payment.
3. Shop the rate. Each point of APR moves the affordable price by roughly 9–10% on a 30-year loan. A 6.75% quote and a 5.75% quote on the same income are different houses.
Frequently asked questions
Do all lenders use exactly 28/36?
No — it is the conventional-loan baseline. FHA loans allow up to about 31/43, and VA loans use a residual-income test instead. Treat 28/36 as the safe planning number: if the math works there, it works almost everywhere.
Should I count bonuses or overtime as income?
Not for your own planning. Lenders average two years of variable pay and often discount it; you should be stricter — plan the mortgage on base salary and let bonuses fund the down payment or the emergency fund instead.
How long does PMI last?
On a conventional loan, PMI drops off automatically at 22% equity and you can request removal at 20% — sometimes sooner with a new appraisal after the home appreciates. FHA mortgage insurance works differently and usually lasts the life of the loan.
What down payment should I aim for?
20% is the magic line: no PMI, a smaller loan, and the most house per dollar of income. Less than 20% is fine when the math still fits — run both numbers in the calculator and compare what the PMI costs you each month.
Does the 28% include utilities and maintenance?
No — lenders ignore them, which is why 28% can still feel tight. Budget another 1–2% of the price per year for maintenance and repairs on top of the mortgage math, and check utility costs for the specific home before you fall in love with it.
Run your own numbers: the free mortgage affordability calculator applies the 28/36 rule to your income, debts, and down payment — with tax, insurance, HOA, and PMI baked into the monthly payment.