- Official section
- National IV.A: Financing Concepts and Terminology
- Broker weight
- A supporting skill within 10% of the national portion
- Expected scored items
- The current PSI broker outline assigns about 10 of 100 scored national items to Financing
Mortgage qualification math guide
Buyer qualification ratios without memorized cutoffs
Qualification-ratio questions test sorting before division. Gross income belongs below the line. The proposed housing payment and other counted debts belong above it. The arithmetic is simple once you stop treating every monthly expense, every source of income, and every percentage you remember as interchangeable.
Last updated: August 1, 2026
What calculation do you need to make?
Short answer: Housing-expense ratio equals proposed monthly housing expense divided by gross monthly qualifying income. Total DTI equals proposed housing expense plus other counted monthly debts, divided by gross monthly qualifying income. To find a maximum housing payment under two stated ratios, compare income times the housing ratio with income times the total-debt ratio minus other monthly debts; use the smaller result. Annual income is divided by 12 before a monthly ratio. Residual income is monthly income minus total monthly debt obligations. Ratio limits and debt treatment vary by product and current underwriting rules, so use the percentages and definitions stated in the problem rather than memorizing one universal cutoff.
The current PSI broker outline places loan calculations and underwriting within Financing, while Real Estate Math separately names other formula families. This guide treats qualification ratios as a financing support skill. Actual creditors verify income, assets, employment, credit history, property obligations, simultaneous loans, current debts, alimony, child support, and other facts under applicable law and product guidance. A correct ratio does not guarantee approval, affordability, or a particular rate. This is exam preparation, not lending or financial advice. Sources were checked through August 1, 2026.
How do you solve buyer qualification ratios?
- Box the requested result: housing ratio, total DTI, gross monthly income, maximum housing payment, or residual income.
- Convert all qualifying income to a monthly gross amount and exclude facts the problem says are not used.
- Build the proposed housing payment from principal, interest, taxes, insurance, and every other required housing item stated.
- List counted nonhousing obligations by monthly payment, not outstanding balance, unless a special formula is supplied.
- Divide housing by income for the front ratio and total obligations by income for total DTI.
- For maximum payment, calculate both stated ratio ceilings and use the smaller housing result.
- Keep ratios as decimals during multiplication, convert quotients to percentages, and retain full precision until the final answer.
- Check that the answer uses gross income, includes each debt once, and does not turn a problem ratio into a universal approval promise.
- Unknown
- Gross monthly income
- Formula
- Annual qualifying income / 12
- Exam safeguard
- Use before-tax amount
- Unknown
- Housing ratio
- Formula
- Housing expense / gross monthly income x 100
- Exam safeguard
- Include stated housing items
- Unknown
- Total DTI
- Formula
- Total monthly obligations / gross monthly income x 100
- Exam safeguard
- Add housing and other debts
- Unknown
- Housing cap
- Formula
- Income x decimal housing ratio
- Exam safeguard
- This is one ceiling
- Unknown
- Total debt cap
- Formula
- Income x decimal total ratio
- Exam safeguard
- Includes proposed housing
- Unknown
- Housing allowed by total ratio
- Formula
- Total debt cap - other counted debts
- Exam safeguard
- Subtract nonhousing debts once
- Unknown
- Ratio-based housing maximum
- Formula
- Smaller of two housing ceilings
- Exam safeguard
- Other underwriting still applies
- Unknown
- Residual income
- Formula
- Monthly income - total monthly obligations
- Exam safeguard
- Report dollars
- Unknown
- Missing income
- Formula
- Monthly obligations / decimal ratio
- Exam safeguard
- Multiply back to check
- Unknown
- Monthly annual charge
- Formula
- Annual charge / 12
- Exam safeguard
- Convert before totaling
Can you follow the calculation from facts to answer?
Calculate both qualification ratios
Scenario: A buyer has $96,000 in annual qualifying income. Proposed housing expense is $2,400 per month, and other counted debts total $900 per month. Find both ratios.
- Gross monthly income is $96,000 / 12 = $8,000.
- Housing ratio is $2,400 / $8,000 = 30%.
- Total DTI is ($2,400 + $900) / $8,000 = 41.25%.
Answer: Housing ratio is 30% and total DTI is 41.25%.
Build housing expense before dividing
Scenario: Monthly principal and interest are $1,850. Annual taxes are $7,200, annual homeowners insurance is $1,440, mortgage insurance is $125 monthly, and association dues are $185 monthly. Gross monthly income is $9,200.
- Monthly taxes are $600 and monthly homeowners insurance is $120.
- Housing expense is $1,850 + $600 + $120 + $125 + $185 = $2,880.
- $2,880 / $9,200 = 0.313043..., or about 31.30%.
Answer: The housing-expense ratio is about 31.30%.
Find the binding ratio ceiling
Scenario: A problem gives $9,000 gross monthly income, a 28% housing ratio, a 36% total ratio, and $650 in other counted monthly debts. What housing payment do the stated ratios permit?
- Housing-ratio ceiling is $9,000 x 0.28 = $2,520.
- Total debt ceiling is $9,000 x 0.36 = $3,240; subtract $650 to leave $2,590 for housing.
- The smaller result is $2,520, so the housing ratio binds.
Answer: The ratio-based maximum housing payment is $2,520.
Recover required gross income
Scenario: Total monthly obligations are $3,600 and the problem requires total DTI not to exceed 40%. What gross monthly income supports that amount at exactly 40%?
- Convert 40% to 0.40.
- $3,600 / 0.40 = $9,000.
- Check: $3,600 / $9,000 = 40%.
Answer: Required gross monthly income is $9,000, or $108,000 annually.
Use monthly payments instead of balances
Scenario: A buyer has a $22,000 auto balance with a $475 monthly payment, a $9,000 card balance with a $180 stated monthly payment, a $225 student-loan payment, and $2,300 proposed housing expense. Gross monthly income is $8,000.
- Counted monthly obligations are $475 + $180 + $225 + $2,300 = $3,180.
- Do not add the $22,000 and $9,000 balances to a monthly numerator.
- $3,180 / $8,000 = 0.3975, or 39.75%.
Answer: The total DTI is 39.75% under the stated debt treatment.
Compare DTI and residual income
Scenario: A borrower has $7,500 in monthly qualifying income and $3,000 in total monthly debt obligations. Find DTI and the simplified Regulation Z residual amount.
- DTI is $3,000 / $7,500 = 0.40, or 40%.
- Residual income is $7,500 - $3,000 = $4,500.
- One result is a percentage and the other is a dollar amount.
Answer: DTI is 40% and monthly residual income is $4,500.
Which math errors cost the most points?
- Trap
- Use take-home pay as the denominator.
- Correction
- Qualification ratios use gross monthly qualifying income when the problem follows the standard DTI setup.
- Trap
- Divide annual debt by monthly income.
- Correction
- Convert numerator and denominator to the same monthly period before dividing.
- Trap
- Use only principal and interest as housing expense.
- Correction
- Add the taxes, insurance, mortgage insurance, dues, and other housing items the problem includes.
- Trap
- Use loan and credit-card balances in the DTI numerator.
- Correction
- DTI uses qualifying monthly obligations, not the total outstanding balances.
- Trap
- Exclude the proposed mortgage from total DTI.
- Correction
- Total DTI includes the proposed housing obligation plus other counted debts.
- Trap
- Add existing debts twice when finding maximum housing.
- Correction
- Subtract nonhousing debts once from the total-debt ceiling; the housing ceiling already concerns housing alone.
- Trap
- Choose the larger result from the two stated qualification ratios.
- Correction
- The smaller housing amount is the binding ratio-based ceiling.
- Trap
- Treat a 40% ratio as 40 in multiplication.
- Correction
- Convert 40% to 0.40 before multiplying by income.
- Trap
- Call residual income a percentage.
- Correction
- Residual income is the dollar amount remaining after monthly obligations are subtracted.
- Trap
- Memorize one DTI cutoff as federal law for every mortgage.
- Correction
- Current Regulation Z does not prescribe one DTI threshold for every covered transaction.
- Trap
- Assume a passing ratio guarantees approval.
- Correction
- Credit, assets, property, product, documentation, and other requirements still matter.
- Trap
- Discount reliable income because of a protected characteristic or disfavored source.
- Correction
- Apply Regulation B and consistent underwriting standards to source, amount, and probable continuance.
Can you solve these original problems?
These questions are original study items aligned to the published outline. They are not copied, recalled, or predicted PSI questions.
1. A borrower has $8,000 gross monthly income and $2,400 proposed housing expense. What is the housing ratio?
- 30%
- 24%
- 33.33%
- 70%
Show answer and explanation
Answer: 30%
$2,400 / $8,000 = 0.30, or 30%.
2. Housing expense is $2,200, other counted debts are $800, and gross monthly income is $7,500. What is total DTI?
- 40%
- 29.33%
- 10.67%
- 44%
Show answer and explanation
Answer: 40%
Total obligations are $3,000, and $3,000 / $7,500 = 40%.
3. A borrower earns $108,000 annually. What is gross monthly income before adding other qualifying sources?
- $9,000
- $8,100
- $2,076.92
- $12,000
Show answer and explanation
Answer: $9,000
$108,000 / 12 = $9,000.
4. Gross monthly income is $10,000, the stated total ratio is 40%, and other counted debts are $900. What housing amount remains under that ratio?
- $3,100
- $4,000
- $4,900
- $3,600
Show answer and explanation
Answer: $3,100
$10,000 x 0.40 = $4,000 total obligations; $4,000 - $900 = $3,100.
5. Which statement about mortgage DTI limits is accurate?
- Different products and creditors can use different limits
- Federal law sets one ratio for every loan
- A passing ratio guarantees approval
- DTI uses net take-home income
Show answer and explanation
Answer: Different products and creditors can use different limits
Current ability-to-repay rules require consideration of repayment ability but do not impose one DTI threshold on every covered mortgage.
Which numbers and formulas are easy to confuse?
- Terms
- Gross income vs. net income
- Difference
- Gross income is measured before taxes and payroll deductions. Net income is take-home pay after deductions.
- Question cue
- Qualification denominator versus paycheck deposit.
- Terms
- Housing ratio vs. total DTI
- Difference
- Housing ratio uses the proposed housing obligation. Total DTI adds counted nonhousing monthly debts to that obligation.
- Question cue
- Home payment only versus all counted debt.
- Terms
- PITI vs. qualifying housing expense
- Difference
- PITI contains principal, interest, taxes, and insurance. Qualifying housing expense can also include mortgage insurance, association dues, ground rent, or other required housing obligations.
- Question cue
- Four-letter core versus underwriting total.
- Terms
- Debt balance vs. monthly debt payment
- Difference
- Balance is the amount owed. DTI normally uses the qualifying monthly obligation determined under the stated rule.
- Question cue
- Outstanding principal versus monthly numerator item.
- Terms
- Qualifying income vs. all cash receipts
- Difference
- Qualifying income meets verification and continuance rules. Cash receipts can include amounts a program does not use for qualification.
- Question cue
- Underwritten income versus money received.
- Terms
- DTI vs. residual income
- Difference
- DTI is debt divided by income and reported as a percentage. Residual income is income minus debt and reported as dollars.
- Question cue
- Relative burden versus dollars remaining.
- Terms
- Maximum ratio vs. actual approval
- Difference
- A stated ratio creates one qualifying ceiling. Approval also depends on credit, assets, product, property, documents, and other requirements.
- Question cue
- Math limit versus full decision.
- Terms
- Front-ratio capacity vs. back-ratio capacity
- Difference
- The front path limits housing directly. The back path limits all debts, then leaves a remainder after existing nonhousing obligations.
- Question cue
- Direct housing cap versus remaining debt capacity.
- Terms
- Income source vs. income reliability
- Difference
- A lawful income source cannot be discounted on a prohibited basis. Its amount and probable continuance can still be evaluated under consistent standards.
- Question cue
- Protected treatment versus underwritten stability.
- Terms
- Qualification vs. affordability
- Difference
- Qualification applies a creditor's lending standards. Personal affordability also considers goals and expenses that the ratio may not capture.
- Question cue
- Eligible loan versus comfortable budget.
What does the outline expect you to calculate?
- Topic
- Gross monthly income
- What to know
- Annual salary, monthly salary, hourly income, weekly income, biweekly income, semimonthly income, overtime, bonus, commission, self-employment, rental income, gross amount, qualifying amount, and before-tax income
- Best exam move
- Convert every qualifying income source to the same monthly period before adding it to the denominator.
- Topic
- Annual-to-monthly conversion
- What to know
- Annual income, 12 months, monthly income, weekly pay, 52 weeks, biweekly pay, 26 periods, semimonthly pay, 24 periods, hourly rate, hours per week, and calculator sequence
- Best exam move
- Use the pay frequency stated; annual income divided by 12 is not the same setup as one paycheck multiplied by two.
- Topic
- Stable qualifying income
- What to know
- Current income, reasonably expected income, verification, third-party record, probable continuance, variable income, history, average, declining income, assets, employment, and program definition
- Best exam move
- Use the qualifying income supplied by the problem and do not automatically count every cash inflow.
- Topic
- Housing-expense ratio
- What to know
- Front-end ratio, proposed housing payment, gross monthly income, percentage, PITI, mortgage insurance, association dues, ground rent, subordinate housing payment, numerator, and denominator
- Best exam move
- Divide the full housing obligation defined by the problem by gross monthly qualifying income.
- Topic
- Principal and interest
- What to know
- Qualifying payment, note rate, fully indexed rate, introductory rate, fixed payment, adjustable payment, amortization, balloon, interest-only feature, loan term, and supplied monthly amount
- Best exam move
- Use the qualifying monthly principal-and-interest figure supplied rather than attempting an unstated amortization calculation.
- Topic
- Taxes and insurance
- What to know
- Annual property tax, monthly property tax, homeowners insurance, flood insurance, mortgage insurance, annual premium, divide by 12, escrow, direct payment, and housing obligation
- Best exam move
- Convert annual amounts to monthly figures before building the housing numerator.
- Topic
- Association and housing charges
- What to know
- Condominium assessment, homeowners association dues, cooperative fee, ground rent, special assessment, subordinate mortgage, leasehold payment, monthly obligation, included portion, and program rule
- Best exam move
- Add the housing-related charges the question includes even when they are not one of the four PITI letters.
- Topic
- Total debt-to-income ratio
- What to know
- Back-end ratio, total monthly obligations, proposed housing, recurring debt, gross monthly income, percentage, borrower, co-borrower, joint application, numerator, and division
- Best exam move
- Add housing and every counted nonhousing obligation before dividing once by gross monthly income.
- Topic
- Installment debt
- What to know
- Auto loan, personal loan, student loan, furniture loan, remaining payments, monthly payment, payoff, deferred payment, lease, co-signed debt, contingent liability, and program treatment
- Best exam move
- Use the monthly obligation and inclusion rule stated, not the account balance as the numerator.
- Topic
- Revolving debt
- What to know
- Credit card, line of credit, minimum payment, reported payment, balance, no payment shown, utilization, payoff, recurring charge, monthly obligation, and program formula
- Best exam move
- Count the qualifying monthly payment supplied or calculated under the question's stated rule, not the full balance.
- Topic
- Support obligations
- What to know
- Alimony, child support, separate maintenance, court order, duration, monthly payment, deduction from income, debt treatment, consistent receipt, disclosure, and underwriting rule
- Best exam move
- Follow the problem's direction for treating the obligation and never subtract it from income and add it as debt in the same calculation.
- Topic
- Simultaneous loans
- What to know
- First mortgage, second mortgage, HELOC, purchase-money note, bridge loan, payment, draw at consummation, monthly obligation, known loan, and ability to repay
- Best exam move
- Include the simultaneous-loan payment when the stated ability-to-repay or program rule requires it.
- Topic
- Maximum housing by front ratio
- What to know
- Gross monthly income, stated housing ratio, decimal percentage, maximum housing expense, multiplication, ceiling, PITI, association dues, and reverse calculation
- Best exam move
- Multiply monthly income by the stated decimal housing ratio to find this ceiling.
- Topic
- Maximum housing by total ratio
- What to know
- Gross monthly income, stated total ratio, maximum total obligations, existing monthly debts, subtraction, remaining housing capacity, lower result, and qualification ceiling
- Best exam move
- Multiply income by the total ratio, then subtract counted debts that are not part of the proposed housing payment.
- Topic
- Two-ratio comparison
- What to know
- Housing ceiling, total-debt ceiling, other debts, smaller result, binding ratio, qualifying payment, answer choice, affordability, and other underwriting limits
- Best exam move
- Calculate both paths independently and choose the smaller allowable housing amount.
- Topic
- Residual income
- What to know
- Monthly income, total monthly obligations, subtraction, dollars remaining, household expenses, family size, region, program standard, DTI comparison, and compensating factor
- Best exam move
- Report residual income in dollars unless the problem separately asks for a ratio.
- Topic
- No universal cutoff
- What to know
- Regulation Z, reasonable ability to repay, no prescribed DTI threshold, creditor standard, loan product, automated underwriting, manual underwriting, compensating factor, reserve, and current guidance
- Best exam move
- Use the ratios in the problem and reject answers claiming one federal percentage approves every applicant.
- Topic
- Fair lending boundary
- What to know
- Regulation B, prohibited basis, consistent standard, part-time income, retirement income, public assistance, marital status, age, reliable income, probable continuance, and individual evaluation
- Best exam move
- Apply neutral qualification math consistently and do not alter income or standards because of a protected characteristic.
How should you drill this calculation?
- Session
- Session 1
- Focus
- Normalize monthly income
- Proof you are ready
- Convert 30 annual, monthly, semimonthly, biweekly, weekly, and hourly income facts to gross monthly amounts.
- Session
- Session 2
- Focus
- Build housing expense
- Proof you are ready
- Assemble 20 principal, interest, tax, insurance, mortgage-insurance, dues, and ground-rent scenarios.
- Session
- Session 3
- Focus
- Classify monthly obligations
- Proof you are ready
- Sort 40 installment, revolving, student, support, lease, simultaneous-loan, and household-expense facts under supplied rules.
- Session
- Session 4
- Focus
- Calculate both ratios
- Proof you are ready
- Solve 15 housing-ratio and 15 total-DTI problems, labeling every numerator and denominator.
- Session
- Session 5
- Focus
- Reverse the ratios
- Proof you are ready
- Find missing income and compare housing and total-debt ceilings in 20 maximum-payment problems.
- Session
- Session 6
- Focus
- Complete a mixed qualification set
- Proof you are ready
- Score at least 90% and justify each answer by time period, income base, housing components, debt treatment, ratio, residual amount, and boundary.
Do not count recognition as mastery. Close the notes and explain the rule, apply it to a new fact pattern, and identify why each distractor fails.
Build speed without skipping the setup
From concept to decision
Drill this topic, then review the explanation
Pass Illinois gives you original national and Illinois questions, topic-by-topic study, clear explanations, timed practice, flashcards, progress tracking, and Math Coach. Start free, find the weak distinction, and focus the next session there.
Questions students ask about Buyer Qualification Ratios and DTI Examples
What is the debt-to-income ratio formula?
Total DTI equals total monthly debt obligations divided by gross monthly qualifying income, multiplied by 100. If housing expense is $2,400, other counted debts are $900, and gross monthly income is $8,000, DTI is $3,300 divided by $8,000, or 41.25%.
What is the housing-expense ratio formula?
The housing-expense ratio, often called a front-end ratio, equals the proposed monthly housing obligation divided by gross monthly qualifying income, multiplied by 100. Use the housing components defined by the problem or loan program, not only principal and interest.
How do you convert annual income to gross monthly income?
Divide the annual qualifying income by 12. An annual amount of $96,000 equals $8,000 per month. Do not divide by 52 unless the question first asks for weekly income, and do not subtract payroll taxes when the formula calls for gross income.
What belongs in the proposed housing expense?
Use the components stated by the question or applicable program. A typical exam setup can include principal, interest, property taxes, homeowners insurance, mortgage insurance, association dues, ground rent, and payments on simultaneous housing debt. Do not assume literal PITI is always the full qualifying payment.
Which monthly debts count in DTI?
Count the obligations the problem identifies under its underwriting rule, such as housing expense, installment payments, revolving debt, student loans, leases, support obligations, and simultaneous loans. Actual treatment depends on duration, documentation, payoff, deferral, and program rules, so a broker-exam shortcut is not universal underwriting policy.
Is there one legal maximum DTI for every mortgage?
No. Current Regulation Z ability-to-repay rules do not prescribe one DTI threshold for every covered loan. Products, creditors, automated findings, compensating factors, and current agency guidance can differ. An exam calculation should provide the qualifying ratios it expects you to use.
How do you calculate the maximum housing payment from two ratios?
First multiply gross monthly income by the stated housing ratio. Then multiply income by the stated total-debt ratio and subtract existing counted monthly debts. The smaller of those two housing amounts is the ratio-based maximum, before any other underwriting limits.
What is residual income?
For the Regulation Z comparison, monthly residual income is monthly income remaining after total monthly debt obligations are subtracted. It is a dollar amount, not a percentage. A creditor can consider DTI, residual income, and other relevant factors under current rules.
Can a lender discount income because it is part-time or retirement income?
Regulation B prohibits discounting or excluding income merely because of a prohibited basis or because income comes from part-time work, an annuity, pension, or retirement benefit. A creditor may evaluate amount and probable continuance under lawful, consistently applied standards.
Are these official Illinois broker exam questions?
No. They are original calculations aligned to the PSI broker outline effective June 24, 2026. Current CFPB regulations and guidance and current Fannie Mae selling guidance were checked through August 1, 2026.
Primary sources
- PSI Illinois Candidate Information Booklet dated June 24, 2026
- Consumer Financial Protection Bureau, current debt-to-income ratio explanation
- 12 CFR 1026.43, current ability-to-repay and DTI or residual-income rules
- 12 CFR 1002.6, current fair-credit application evaluation rules
- Fannie Mae Selling Guide B3-6-02, current debt-to-income ratio guidance
- Fannie Mae Selling Guide B3-6-05, current monthly debt-obligation guidance
- Consumer Financial Protection Bureau, current Qualified Mortgage explanation
The current official outline controls the tested scope. Statutes, regulations, and official agency materials control when a general study rule and a jurisdiction-specific rule differ.
Editorial status
Checked against primary sources
The Pass Illinois editorial team last checked this guide on August 1, 2026. Every practice question is an original study item, and the source links above let you verify the rules that support the lesson.