The house fits. The loan does not.
Begin with a house that costs $100,000.
This is a thought experiment: a buyer with $20,000 for the down payment, seeking an $80,000 mortgage. Keep the transaction ordinary enough that we can see where it becomes difficult.
At an assumed fixed rate of 7 percent over 30 years, the principal-and-interest payment would be about $532 a month. That is arithmetic, not a rate offer. Taxes, insurance, maintenance, closing costs and the buyer's other obligations still need to be accounted for. The down payment is not all the cash the purchase will require. The CFPB's Loan Estimate guide distinguishes these separate costs for good reason. Loan Estimate explainer
For now, suppose the house is sound, the title is clear and the household can support the full cost. Suppose, in other words, that we have not hidden the usual affordability problems inside a conveniently small payment.
Would the buyer necessarily be able to get the loan?
We tend to imagine mortgage access as a test of the person applying. The lender looks at income, debts, savings and credit, then decides whether the applicant can be trusted with the money.
But another calculation sits beside that one. Will the transaction be worth doing for the business that must arrange it?
The first question concerns the buyer's capacity to pay. The second concerns the lender's capacity to earn. A smaller balance may help the first while making the second harder.
This is the uncomfortable possibility at the inexpensive end of American housing: the home can become cheaper without becoming easier to buy.
The problem is not that every $100,000 house deserves a mortgage. It is that price alone tells us less about access than we think.

