How lenders decide how much house you can afford
Most lenders size a mortgage with two debt-to-income (DTI) ratios. The front-end ratio caps your total housing payment — principal, interest, property tax, insurance, HOA and PMI, together called PITI — at a share of gross monthly income, traditionally 28%. The back-end ratio caps housing plus all other monthly debt payments at 36%. Whichever limit is tighter wins, and that becomes your maximum monthly payment. On $100,000 a year with $500 of other debts, the front-end limit is $2,333 and the back-end limit is $2,500, so $2,333 is the number that matters.
Turning a payment into a price takes one more step, because property tax and PMI scale with the price while insurance and HOA are fixed. The calculator solves the equation directly: price = (max payment − insurance − HOA + down payment × k) ÷ (k + tax rate ÷ 12 + PMI adjustment), where k is the monthly payment factor for your rate and term. With a $40,000 down payment at 6.5% over 30 years and 1.2% property tax, that $2,333 payment supports a home of roughly $320,000 — PMI included, since $40,000 is under 20% of that price.
The down payment matters twice. It lowers the loan you need for a given price, and if it is under 20% of the price most conventional lenders add private mortgage insurance, typically 0.3–1.5% of the loan per year, which eats into the same payment budget. The calculator applies PMI automatically only when the resulting loan-to-value is above 80%.
Approved is not the same as comfortable. The 28/36 rule is a lending limit, not budgeting advice. Many buyers aim for a payment closer to 20–25% of gross income to leave room for maintenance, childcare, retirement savings and rate risk. Try the conservative and aggressive presets to see how wide the approvable range really is, then pick a number you would still be happy with in a tight year.