How Much House You Can Afford (I Ran the Lender Math)
By De Van Do -- May 26, 2026 -- 9 min read
Three Questions People Ask as One
How much house can I afford is really three separate questions wearing a single sentence.
What will a lender approve me for. How much cash do I need on the table to close. And what will the actual monthly cost be once every line item is included.
They have different answers and they fail in different ways. People get approved and then discover they are short on cash. People assemble the cash and then discover the monthly payment is a third higher than the mortgage payment they budgeted around.
So I built the first-time buyer calculator to answer all three at once, then ran a realistic scenario end to end to see what falls out. The numbers below are what the tool produces, and I have included the intermediate steps so you can follow the logic rather than trust the output.
The Household I Modeled
A $90,000 annual income, which is $7,500 a month gross. Five hundred dollars a month of existing debt payments. Ten percent down. A 7% rate on a 30 year fixed. Property tax at 1.1% and homeowners insurance at $150 a month, the same assumptions the rest of this site uses.
That is a fairly ordinary dual-income household with one car payment, and it is close to the national median for a first-time buyer.
One thing to flag before the results. This models what a lender will approve, which is a ceiling, not a recommendation. The gap between those two is the most important idea in this article and I come back to it at the end.
Question One: The Lender Maximum
The qualification math runs in stages.
Gross monthly income of $7,500 gives a front-end housing ceiling of 28%, which is $2,100. The back-end ceiling of 43% gives $3,225, and after the $500 of existing debt that leaves $2,725. The lender takes the smaller of the two, so $2,100 is the working number.
Out of that $2,100 comes $150 of insurance and about $253 of monthly property tax, leaving roughly $1,697 for principal and interest.
At 7% over 30 years, that payment supports a loan of about $248,229. With 10% down, that is a maximum purchase price of about $275,810.
The actual monthly breakdown at that price: $1,651 of principal and interest, $253 of property tax, $150 of insurance, and $145 of PMI, for an all-in figure of about $2,199.
Write down both of those numbers. The price is what you shop with. The $2,199 is what you actually live with, and it is the one that determines whether the house is comfortable or a trap.
Question Two: The Cash
This is where approvals go to die, and it is the number almost nobody estimates correctly in advance.
On a $275,810 purchase, the 10% down payment is about $27,581.
Closing costs at 3.5% of the price come to about $9,653. That covers origination, appraisal, title work, recording, and prepaid escrow items.
Add a $5,000 allowance for moving, immediate repairs, and the things that always appear in the first month.
Total cash needed: about $42,234.
The down payment is only 65% of that. Most people budget the down payment and treat everything else as a rounding error, then find themselves roughly fifteen thousand dollars short three weeks before closing. If you have $28,000 saved and you are shopping at $275,000, you are not ready yet, even though you are fully approved.
And this is before reserves. Many lenders want to see a few months of payments still in the account after closing. Arriving at the table with exactly enough is a weaker file than arriving with a cushion.
Question Three: What Actually Moves the Number
I varied one input at a time to see which lever matters most. The results were not evenly distributed.
The rate moved it most. At 5% the same household qualifies for about $327,033. At 6%, $299,990. At 7%, $275,810. At 8%, $254,294. That is a swing of about $72,739 in buying power between 5% and 8% on an identical income, and it is the one variable you have the least control over.
Income moved it proportionally, as you would expect. $75,000 supports about $226,305, and $150,000 supports about $473,827.
The down payment moved it far less than people assume. Going from 5% down to 20% down raises the maximum price only from about $263,779 to about $303,275, a gain of roughly $39,496. But the cash required goes from about $27,421 to about $76,270. You are spending an extra $48,849 in cash to buy $39,496 of additional house.
And the existing debt, in this scenario, moved it by nothing at all. That is not an error, and it has its own explanation.
Why Your Car Payment Did Not Matter
It is worth understanding, because it inverts the standard pre-application advice.
The back-end ratio only starts to constrain you once your monthly debts exceed the gap between the two ceilings, which is 43% minus 28%, or 15% of gross income. On $7,500 a month that is $1,125.
The $500 car payment in this scenario sits well under that. It is invisible. Paying it off before applying would not raise the approval by a dollar, and it would convert cash you need for closing into equity in a car.
Above $1,125 the picture flips hard. At $1,500 of monthly debt the maximum price falls to about $222,769. At $2,000 it falls to $152,049.
So the correct move depends entirely on which side of that line you are on. Multiply your gross monthly income by 0.15 and compare. It takes ten seconds and it decides whether the most common piece of pre-approval advice applies to you at all. The full mechanics are in the DTI article on this site.
The Number the Calculator Will Not Give You
Everything above is the lender maximum. I want to be direct about what that is and is not.
It is an underwriting ceiling derived from gross income, before tax, before retirement contributions, before health insurance, and before every recurring cost that is not a debt obligation. It does not know you have two children in daycare. It does not know your commute costs $400 a month. It does not know you want to keep saving.
At $2,199 a month all-in, this household is spending 29.3% of gross on housing. On a take-home of perhaps $5,600, that is closer to 39% of the money that actually arrives.
A common and sensible adjustment is to run the calculation against take-home pay rather than gross, or simply to shop at 80% to 85% of the approved maximum. In this scenario that would mean looking at houses around $220,000 to $235,000 rather than $275,810.
Nobody has ever regretted buying slightly less house than they qualified for. The reverse is one of the most common financial regrets there is.
The Input That Costs More Than It Looks
One variable I have not mentioned moves the cash side more than the price side, and it deserves a section of its own: your credit score.
It does not enter the DTI arithmetic at all. It enters through the rate you are quoted, and the rate is the single biggest lever on buying power. The swing between 5% and 8% was about $72,739 in this scenario, and a credit tier is worth a meaningful fraction of that range on any given day.
It also drives PMI pricing, which is graded by score and loan-to-value together. The same 10% down loan can carry very different mortgage insurance depending on which side of a score threshold you land on, and those thresholds tend to sit at round numbers.
So the sequence matters. Improving a score from the high 600s to the mid 700s can be worth more to your purchasing power than saving another $10,000, and it is usually faster. Paying down revolving balances to under 30% of their limits moves a score within a billing cycle or two. Opening a new card or financing furniture before closing moves it the other way, which is why lenders re-pull credit just before funding.
The calculator asks for your score because it feeds the readiness diagnostic rather than the price ceiling. Treat a low score as the first thing to fix, not the last.
Run Your Own Three Numbers
Put your real figures into the first-time buyer calculator: gross annual income, total monthly debt payments, savings, credit score, and the down payment percentage you are actually planning.
Then read three outputs rather than one.
The maximum price tells you what a lender will approve. The cash needed tells you whether you can close on it, and it is usually the binding constraint for first-time buyers. The all-in monthly tells you what your life will cost afterward.
Then do the part no calculator can do. Take that all-in monthly figure, subtract it from your actual take-home pay, and look at what remains against the rest of your real spending. If the answer is uncomfortable, the approval amount is not the number to shop with.
Buy at the number that leaves your life intact, not the number the ceiling allows.
Run your own affordability numbers
Lender maximum, cash needed at closing, and the all-in monthly payment on one screen.
Related guides
The DTI Rule That Actually Binds (I Tested Both Ratios)
Lenders quote two DTI limits, 28% and 43%. I ran both through my own calculator and found that on a typical income the second one does nothing at all until your monthly debts pass a specific threshold.
Down Payment Strategies: How Much to Put Down and Where to Get It
A complete guide to down payment strategies -- 3% vs 5% vs 20%, how to save faster, gift funds, down payment assistance programs, and the PMI math.
First-Time Homebuyer Guide: Everything You Need to Know in 2025
A complete step-by-step guide for first-time homebuyers -- from checking your finances to getting the keys, including programs and mistakes to avoid.
About the author
De Van Do has a background in technology and built VisualMortgage out of curiosity about making mortgage math transparent. De Van Do is not a licensed loan officer or mortgage broker -- for advice specific to your situation, consult a licensed mortgage professional. Read more about VisualMortgage.