Lending Math
Qualifying Ratios: Housing and Total Debt
Ratio ceilings are set by the loan program, the agency or investor behind it, and the lender's own overlays, and they are revised periodically. Work from the current underwriting guidelines for the program in question rather than from a remembered pair of numbers, and answer exam items using whatever thresholds the question supplies.
Underwriting reduces a borrower's capacity to two fractions. One compares the proposed housing payment to income. The other compares every recurring obligation, housing included, to that same income. An applicant has to clear both.
Exam items on this topic are arithmetic wearing a story. The arithmetic is division. The scoring happens in the setup: what goes on top, what goes on the bottom, and which of the two limits binds.
What Each Fraction Measures
The housing ratio, often labeled the front ratio, puts the full proposed monthly shelter obligation over gross monthly income. Shelter obligation means more than loan repayment: add the principal and interest, the escrowed property tax, the hazard premium, mortgage insurance where it applies, and any association assessment on the unit. Leave utilities and upkeep out; they are real costs but they are not underwritten here.
The total debt ratio, the back ratio, keeps that same shelter figure and adds the borrower's other recurring liabilities on top: installment loans, revolving minimum payments, student obligations, and court-ordered support. Then it divides by the identical income figure. Because the shelter number appears in both, the back ratio can never come out lower than the front ratio.
Gross means before withholding, and it means documented and stable. Overtime, bonus, commission and self-employment earnings enter only when the file supports an average the program will accept. Swapping in net pay is the single most reliable way to get an otherwise correct calculation marked wrong.
Sorting the Inputs Before You Divide
Most missed items are sorting errors, not division errors. Work through the fact pattern once and assign every dollar a place.
Shelter numerator. Loan repayment, escrowed taxes, hazard coverage, any required mortgage insurance, and association dues on the subject property. This entire figure repeats inside the back ratio.
Other liabilities. Recurring obligations that survive closing. Installment balances near payoff, obligations another party is legally and demonstrably paying, and one-off bills are treated differently from program to program, so follow what the question states.
Denominator. Gross monthly income for every borrower on the note, before tax. Convert annual figures by dividing by twelve and hourly figures by the documented schedule the question gives you.
Excluded items. Utilities, groceries, insurance premiums unrelated to the property, and voluntary retirement contributions sit outside both fractions.
The binding limit. Run both ratios against both ceilings. The lower of the two resulting payment allowances governs, because an applicant who fails either fraction fails the file.
Working Backward to a Maximum Payment
Half of the items on this topic run in reverse. Instead of handing you a payment and asking for the percentages, they hand you the percentages and ask how large a shelter obligation the borrower can carry.
Take the housing ceiling first: multiply gross monthly income by that percentage and you have one candidate allowance. Then take the total debt ceiling: multiply income by that percentage and subtract the borrower's other recurring obligations, because those consume part of the same capacity. You now have a second candidate allowance.
Report the smaller of the two. Which one wins depends on how heavily the borrower is already obligated. A borrower carrying almost no other debt is usually capped by the housing fraction; a borrower carrying a car note and a card balance is usually capped by the total debt fraction. Candidates who average the two, or who answer with whichever they computed first, lose the item even though both computations were right.
Then read what the question actually wants back. A maximum shelter obligation is not a maximum loan amount, and it is not a maximum purchase price. Converting further requires the tax, insurance and assessment figures to be stripped out and a rate and term applied, which is a separate step the item will ask for explicitly if it wants it.
Two Problems to Run
Original practice items, written for this page. Figures are illustrative; use the thresholds each problem states rather than any you have memorized.
Question 1
An applicant grosses $96,000 a year. The proposed shelter obligation, including escrowed tax and hazard coverage, is $2,040 a month, and the applicant pays $310 a month on an auto note. The program in this question caps the housing fraction at 28 percent and the total debt fraction at 36 percent. Does the file clear both?
Convert income first: $96,000 divided by 12 is $8,000 a month. Housing fraction: $2,040 over $8,000 is 25.5 percent, inside the 28 percent cap. Total debt fraction: $2,040 plus $310 is $2,350; $2,350 over $8,000 is 29.375 percent, inside the 36 percent cap. Both clear, so the file qualifies on ratios. Note that the shelter figure was counted once in the first fraction and again inside the second.
Question 2
A second applicant grosses $6,400 a month and carries $780 a month in recurring obligations outside housing. Using a 31 percent housing cap and a 43 percent total debt cap, what is the largest shelter obligation this applicant can be approved for?
Housing path: $6,400 times 0.31 is $1,984. Total debt path: $6,400 times 0.43 is $2,752, less the $780 already obligated, leaves $1,972. The binding answer is the smaller figure, $1,972, set by the total debt fraction because the outside obligations are heavy enough to consume part of the capacity. Approving at $1,984 would push the total debt fraction past its cap.
Questions Candidates Ask About Qualifying Ratios
Which components belong in the shelter figure?
Loan repayment, the escrowed property tax, the hazard premium, mortgage insurance if the program requires it, and any association assessment tied to the unit. Utilities, maintenance reserves and moving costs are excluded. Some programs and some exam items label the version that includes association dues separately, so read the abbreviation the question uses rather than assuming.
Why can a borrower fail on one fraction and pass the other?
The two measure different things. A modest shelter obligation paired with heavy card, auto and student obligations produces a comfortable housing fraction and a failing total debt fraction. The reverse happens when a debt-free applicant reaches for an expensive property. Clearing both is required; clearing one is not partial credit.
What are compensating factors and when do they matter?
They are documented strengths an underwriter may cite when approving a file above a standard ceiling: substantial reserves after closing, a long unbroken employment record, a sizable down payment, a strong credit profile, or a new shelter obligation close to the rent already being paid. Whether they are permitted, and how far they stretch a ratio, is set by the program and the lender, not by a rule of thumb.
Does the exam expect specific ceilings to be memorized?
Well-written items supply the ceilings inside the fact pattern, because the published figures differ by program and change over time. Learn the structure of the two fractions and the rule that the tighter limit governs. If an item does reference a program without stating numbers, answer from the guidelines that program currently publishes.
Whose income and whose debts are counted?
Every borrower obligated on the note contributes income, and their recurring obligations count as well. A household member who is not on the loan generally contributes neither. This is worth checking in the fact pattern, since items often introduce a relative or a roommate whose earnings are deliberately irrelevant.
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