House Affordability Calculator

Most mortgage tools start with a price and hand you a payment. This one runs the arrow backwards: it starts with your income, finds the largest housing payment an underwriter would sign off on, and converts that payment into the highest price it can buy. Step one is the two ratio caps. FDIC Money Smart describes lenders requiring PITI to be at or below 25-28% of gross monthly income (the front-end ratio), and housing plus long-term debt to be at or below 33-36% (the back-end ratio). The defaults here are 28% and 36%. Your annual income is divided by twelve, the front-end cap is that figure times your front ratio, and the back-end cap is that figure times your back ratio minus your existing monthly debts — because the CFPB defines debt-to-income with the mortgage inside the ratio, not beside it. The lower of the two caps is what binds, and the result tells you which one it was. If your current car, card and student-loan payments already exceed the back-end ratio on their own, the cap is clamped to zero: negative room is not a smaller house, it is no house. Step two is the inversion. The Regulation Z annuity payment can be divided through by the loan to give k, the monthly payment per dollar borrowed. Read backwards, loan = payment / k. Fixed carrying costs come off your cap first — annual insurance divided by twelve, plus any HOA fee — and what remains is solved for price. Because property tax scales with price and PMI scales with the loan, the housing payment is linear in price, and the solve is a single rearrangement: price = (budget + down payment x (k + pmi/1200)) / (k + pmi/1200 + tax rate/1200). The surprising part is what happens around the 20% down payment line. PMI applies only above 80% loan-to-value, so the cost curve does not rise smoothly with price — it jumps upward at exactly five times your down payment, the price where your cash is precisely 20%. That means some budgets land inside the jump: you can afford a house at exactly 5x your down payment and not one dollar more, because the very next dollar of price triggers a mortgage insurance premium on the whole loan. The solve is therefore run on both sides of that discontinuity and checked for self-consistency, which is why a small change in your savings can move the answer more than you would expect. The price is rounded down to the whole dollar, never up, and every payment component is then re-derived from that rounded price so the breakdown always sums to the reported total and never creeps past the cap. Rounding up would quote you a house you do not qualify for. Two caveats worth holding on to. The 28/36 figures are a rule of thumb, not a legal ceiling: the Fannie Mae Selling Guide sets a 36% maximum total DTI that can be exceeded up to 45% with sufficient credit score and reserves, and up to 50% through Desktop Underwriter — so raise the back ratio to see what a lender might stretch to, but treat the default as what is comfortable. And this is a gross-income calculation, before tax; the payment it blesses can still be more than your take-home comfortably absorbs. Once you have a target price, price the actual payment on the mortgage calculator, and if you are weighing the whole decision rather than just the loan, the rent vs buy calculator is the better starting point.