What affordability means to an underwriter
Affordability is not a feeling about your budget. To a lender it is two arithmetic tests on gross income, and a file passes or fails on them before anyone looks at your bank statements.
The first test is the front-end ratio, sometimes called the housing ratio. It divides your full monthly housing payment — principal, interest, property tax, homeowners insurance, HOA dues and mortgage insurance, the bundle known as PITI — by your gross monthly income. The second is the back-end ratio, which adds every other recurring debt payment on your credit report to the numerator: car loans, student loans, minimum credit-card payments, child support, alimony.
Both use gross income, before tax. That is deliberate and it is also the reason lender numbers feel high. A borrower earning $90,000 sees roughly $5,800 a month land in the account after federal, state and payroll tax, but the ratios are computed against $7,500. A payment that is 28% of gross is closer to 36% of what you actually receive.
The conventional pair of ceilings is 28% and 36%, a rule of thumb that predates automated underwriting and survives because it is easy to remember. FHA underwriting uses 31% and 43%. Automated systems at Fannie Mae and Freddie Mac will approve back-end ratios well above 36% when the file carries compensating strengths — large reserves, a high credit score, a big down payment — so treat the answer here as the conservative benchmark that a manual underwriter would apply, not as a hard cap.
How the price is worked out from the ratios
The calculation runs in four moves, and the awkward one is the last.
One: find the housing budget. Multiply gross monthly income by the front-end ceiling to get one allowance. Multiply it by the back-end ceiling and subtract your existing debt payments to get the other. The smaller of the two is the most housing payment the guideline permits, and which one is smaller is worth knowing: if the back-end is binding, paying off a car loan directly buys purchasing power, whereas if the front-end is binding, retiring debt changes nothing.
Two: strip out everything that is not loan repayment. Property tax, insurance, HOA dues and mortgage insurance all sit inside PITI, so they eat the same budget. On a typical purchase they consume a quarter to a third of it.
Three: invert the amortised-loan formula. The standard payment formula gives a payment from a loan; here you have the payment and want the loan, so you use the annuity factor the other way round: L = M · (1 − (1 + r)−n) / r. At 6% over 30 years that factor is 166.79, so every $1,000 of monthly principal and interest supports $166,792 of loan. The same identity is behind the mortgage payment calculator, read from the other end.
Four: add the down payment. The loan plus your cash is the price.
Step three cannot be done in one pass, because property tax is a percentage of the price and mortgage insurance is a percentage of the loan — both of which are what you are solving for. The calculator handles this by bisection: it guesses a price, computes the full PITI that price implies, and narrows the guess until the PITI lands exactly on the budget.
Worked example: $90,000 income, $500 of debts, $40,000 down
Take the default case — $90,000 of gross household income, $500 a month of existing debt payments, $40,000 of cash, a 6.5% note over 30 years, property tax at 1.1% of price, insurance at $1,800 a year, no HOA, and mortgage insurance at 0.55% of the loan.
- Gross monthly income. $90,000 ÷ 12 = $7,500.
- Front-end allowance. 0.28 × $7,500 = $2,100.
- Back-end allowance. 0.36 × $7,500 = $2,700, less $500 of debts = $2,200.
- Housing budget. min($2,100, $2,200) = $2,100. The front-end ratio binds, by $100 a month.
- Write PITI as a function of price. Monthly payment per dollar of loan at 6.5% over 360 months is 0.00541667 ÷ 0.8569737 = 0.00632068. Mortgage insurance adds 0.0055 ÷ 12 = 0.00045833 per dollar of loan. Property tax is 0.011 ÷ 12 = 0.00091667 per dollar of price, and insurance is $1,800 ÷ 12 = $150 flat. With the loan equal to price minus $40,000, PITI = 0.00677901 × (P − 40,000) + 0.00091667 × P + 150 = 0.00769568 × P − 121.16.
- Set that equal to the budget and solve. 0.00769568 × P − 121.16 = 2,100, so P = 2,221.16 ÷ 0.00769568 = $288,624.
- Split the answer back out. Loan = $288,624 − $40,000 = $248,624. Principal and interest = 248,624 × 0.00632068 = $1,571.47. Property tax = 288,624 × 0.00091667 = $264.57. Insurance = $150.00. Mortgage insurance = 248,624 × 0.00045833 = $113.95.
- Check. 1,571.47 + 264.57 + 150.00 + 113.95 = $2,100.00, exactly the front-end allowance. Back-end DTI is (2,100 + 500) ÷ 7,500 = 34.67%, inside the 36% ceiling.
The down payment is $40,000 of a $288,624 price, or 13.86%, which is why mortgage insurance appears. Reaching 20% is a simultaneous condition, because the price moves with the cash: solving 0.00723735 × P = 1,950 + 0.00632068 × d with no mortgage insurance and d = 0.2P gives d = $65,293 against a price of $326,466.
How to read the answer
Start with the binding constraint, which the calculator names below the results. If the back-end ratio is binding, your existing debts are the lever: every $100 a month of debt payment you retire moves $100 straight into the housing budget, which at 6.5% over 30 years is roughly $15,800 of additional loan. If the front-end ratio is binding, retiring debt does nothing for the price and only income, down payment or a lower rate will move it.
Next look at the down-payment percentage. Below 20% the loan carries mortgage insurance, and on a conventional loan that charge is not permanent — under the Homeowners Protection Act a servicer must cancel it on written request when the scheduled balance reaches 80% of the original value, and terminate it automatically at 78%. FHA loans behave differently: with less than 10% down the annual mortgage insurance premium runs for the life of the loan.
Then treat the number as a ceiling rather than a target. The ratios say nothing about childcare, medical costs, retirement contributions, commuting or the maintenance a house demands and an apartment does not. A common planning discipline is to shop at 80% of the calculated maximum and keep the difference as the reserve that turns a broken furnace into an inconvenience. The rent vs buy calculator is the better tool for asking whether buying at all makes sense at your holding period.
Finally, note what the rate does. The sensitivity table beneath the results holds everything else fixed and varies only the note rate. In the default case, moving the rate from 6.5% to 7.0% drops the maximum price from $288,624 to $278,332, a fall of 3.6% — and the loan itself falls further in percentage terms than the price does, because the down payment is unaffected by the rate.
Maximum loan supported by $1,000 a month of principal and interest
| Annual rate | 15 years | 20 years | 30 years |
|---|---|---|---|
| 5.0% | $126,455 | $151,525 | $186,282 |
| 5.5% | $122,387 | $145,373 | $176,122 |
| 6.0% | $118,504 | $139,581 | $166,792 |
| 6.5% | $114,796 | $134,125 | $158,211 |
| 7.0% | $111,256 | $128,983 | $150,308 |
| 7.5% | $107,873 | $124,132 | $143,018 |
| 8.0% | $104,641 | $119,554 | $136,283 |
This table is principal and interest only. Subtract tax, insurance, dues and mortgage insurance from your housing budget before applying it.
Mistakes that make an affordability estimate wrong
- Using take-home pay. The ratios are defined on gross income. Feeding net pay into a 28% test produces a number roughly a fifth too small.
- Counting only principal and interest. Escrow and mortgage insurance are inside the housing ratio, and on the default case above they take $528.52 of a $2,100 budget — 25% of it.
- Forgetting that the down payment is not all cash needed. Closing costs commonly run 2–5% of the price on top, and money spent there is not available for the down payment.
- Entering the APR instead of the note rate. APR folds fees into a comparison rate; your payment is computed from the note rate, and using the APR understates purchasing power.
- Assuming the tax rate on the listing. Many jurisdictions reassess at sale, so the seller's current tax bill can be well below what you will pay. Use your county's effective rate on the purchase price.
- Ignoring income that will not count. Bonus, commission and self-employment income usually need a two-year history before an underwriter will average it in.
Where this sits among the other tests a lender runs
Debt-to-income is one of three gates, and passing it does not mean an approval. The second is loan-to-value, which caps the loan against the appraised value — and against the lower of price and appraisal, which is why a low appraisal kills deals. The third is credit: score drives both eligibility and price, and a rate quote is only as good as the score band it assumes.
There are also product ceilings this calculator does not know about. Conforming loan limits set the boundary between conventional and jumbo pricing and change annually by county. FHA sets its own county-level maximum. If the price here lands above either, the rate you entered probably no longer applies.
Once you have a price, the follow-on questions are handled elsewhere on the site. The amortization schedule calculator shows how the balance actually retires; the extra payment calculator prices early payoff; and if you are carrying consumer debt that is holding the back-end ratio down, the debt avalanche calculator shows the cheapest order to clear it.
One last framing. This tool answers “what will a lender allow”, which is a different question from “what should I spend”. The ratios were written to protect the loan, not the borrower's retirement account.
Key terms
- Front-end ratio
- Full monthly housing payment divided by gross monthly income. Also called the housing ratio.
- Back-end ratio
- Housing payment plus all other recurring debt payments, divided by gross monthly income. This is what most people mean by “DTI”.
- PITI
- Principal, interest, taxes and insurance — the bundle lenders test against the front-end ratio. HOA dues and mortgage insurance are counted in it even though the acronym omits them.
- Annuity factor
- (1 − (1 + r)−n) / r — the loan amount supported by one dollar of periodic payment. Multiplying by the payment converts a budget into a balance.