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The money
Front-end: your housing payment as a share of gross monthly income. Back-end: housing plus all other monthly debts. Lenders decide with the second one.
Debt-to-income (DTI) ratios are how lenders test whether a payment fits your life. The front-end (housing) ratio divides the full monthly housing cost — principal, interest, taxes, insurance, any HOA — by your gross monthly income. The back-end ratio adds your other monthly debt payments: cards, car loans, student loans.
Back-end is the one that usually decides approval, and it's why paying down a car loan or card can unlock more house than months of extra saving — it lowers the ratio directly.
Each loan type and program publishes its own limits, and compensating factors (reserves, strong credit) can stretch them, so treat any single cutoff you read online as folklore until a lender runs yours.
Source: HUD Housing Counselor Training, Module 4.1 (Homeownership/Pre-Purchase)
Who confirms it for you: A lender computes yours exactly during preapproval.
Educational, not advice — and never an eligibility determination. Program rules and loan requirements change; the cited source and the named confirmer are the authorities for your case.