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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.

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

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?

  1. Box the requested result: housing ratio, total DTI, gross monthly income, maximum housing payment, or residual income.
  2. Convert all qualifying income to a monthly gross amount and exclude facts the problem says are not used.
  3. Build the proposed housing payment from principal, interest, taxes, insurance, and every other required housing item stated.
  4. List counted nonhousing obligations by monthly payment, not outstanding balance, unless a special formula is supplied.
  5. Divide housing by income for the front ratio and total obligations by income for total DTI.
  6. For maximum payment, calculate both stated ratio ceilings and use the smaller housing result.
  7. Keep ratios as decimals during multiplication, convert quotients to percentages, and retain full precision until the final answer.
  8. 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.

  1. Gross monthly income is $96,000 / 12 = $8,000.
  2. Housing ratio is $2,400 / $8,000 = 30%.
  3. 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.

  1. Monthly taxes are $600 and monthly homeowners insurance is $120.
  2. Housing expense is $1,850 + $600 + $120 + $125 + $185 = $2,880.
  3. $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?

  1. Housing-ratio ceiling is $9,000 x 0.28 = $2,520.
  2. Total debt ceiling is $9,000 x 0.36 = $3,240; subtract $650 to leave $2,590 for housing.
  3. 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%?

  1. Convert 40% to 0.40.
  2. $3,600 / 0.40 = $9,000.
  3. 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.

  1. Counted monthly obligations are $475 + $180 + $225 + $2,300 = $3,180.
  2. Do not add the $22,000 and $9,000 balances to a monthly numerator.
  3. $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.

  1. DTI is $3,000 / $7,500 = 0.40, or 40%.
  2. Residual income is $7,500 - $3,000 = $4,500.
  3. 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?

  1. 30%
  2. 24%
  3. 33.33%
  4. 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?

  1. 40%
  2. 29.33%
  3. 10.67%
  4. 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?

  1. $9,000
  2. $8,100
  3. $2,076.92
  4. $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?

  1. $3,100
  2. $4,000
  3. $4,900
  4. $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?

  1. Different products and creditors can use different limits
  2. Federal law sets one ratio for every loan
  3. A passing ratio guarantees approval
  4. 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.

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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

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.

Read our editorial and corrections process

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