Lending Math
Mortgage Qualification Ratios: Real Estate Exam Math
Lenders use two debt ratios to qualify borrowers: front-end ratio (housing only) and back-end ratio (housing + all other debts). Conventional loans typically allow up to 28% front-end and 36% back-end. FHA allows higher.
The Two Ratios
Front-End (Housing) Ratio = (Principal + Interest + Taxes + Insurance + HOA) ÷ Gross Monthly Income × 100. Sometimes called the housing ratio or the 'top' ratio.
Back-End (Total Debt) Ratio = (Housing + Car loans + Student loans + Credit card minimums + Alimony) ÷ Gross Monthly Income × 100.
Typical Maximum Ratios by Loan Type
Conventional: 28% front-end / 36% back-end (28/36)
FHA: 31% front-end / 43% back-end (31/43)
VA: no specific front-end; back-end typically up to 41%
USDA: 29% front-end / 41% back-end (29/41)
Higher ratios may be allowed with strong compensating factors (high credit score, large down payment, reserves)
Two Worked Examples
Question 1
Borrower's gross monthly income: $7,500. Proposed PITI: $1,950. Other debts: $400/month. What are the front-end and back-end ratios? Does this qualify for conventional?
Front-end: $1,950 ÷ $7,500 × 100 = 26%. Back-end: ($1,950 + $400) ÷ $7,500 × 100 = 31.3%. Both under 28/36 — qualifies for conventional.
Question 2
Borrower's gross monthly income: $5,000. Other monthly debts: $600. What's the maximum PITI for FHA (31/43 limits)?
Front-end limit: $5,000 × 31% = $1,550. Back-end limit: $5,000 × 43% − $600 = $2,150 − $600 = $1,550. Maximum PITI is the LOWER of the two: $1,550.
Practice Qualification Math
Drill front-end/back-end ratio problems.
Related Lending Pages
Ratio FAQ
What does PITI mean?
Principal, Interest, Taxes, Insurance — the four basic components of a monthly housing payment. PITIA adds HOA association dues.
Why use the lower ratio limit?
Borrowers must pass BOTH ratios. Lender picks the lower of the two maximums to determine the maximum housing payment.
What are 'compensating factors'?
Strengths that justify approving a borrower above standard ratio limits — high credit score, significant cash reserves, large down payment, stable employment history.