- Official section
- National XI: Real Estate Math
- Broker weight
- About 7 of 100 scored national questions, with math also embedded in other topics
- Expected scored items
- The current PSI broker outline names basic math, property-tax calculations, prorations, commission, seller net, buyer funds, transfer fees, PITI, equity, LTV, points, area, appreciation, depreciation, assessment, mill rate, GRM, and capitalization rate
Real estate math formula sheet
Memorize the relationship, then label the facts
A formula sheet is useful only if it survives a word problem. Learn a compact set of parent relationships, name every input, align the units, and rebuild the variation you need. The exam is not asking whether you can recite letters. It is asking whether you can recognize the base, rate, time period, income level, debt balance, or ledger side hidden inside ordinary transaction language.
Last updated: August 1, 2026
What calculation do you need to make?
Short answer: Start with six families. Percentage: part = total x decimal rate. Closing: buyer funds = buyer uses - buyer credits and sources; seller net = seller credits - seller debits. Financing: LTV = loan / required value; equity = value - debt; points cost = loan x points / 100; PITI = principal and interest + property tax + insurance, plus any stated included assessment or insurance item. Proration: share = periodic amount / stated period x responsible period. Measurement: rectangle area = length x width; triangle = base x height / 2; 43,560 square feet = 1 acre; a nominal section = 640 acres. Income: NOI = effective gross income - operating expenses; cap rate = NOI / value; GRM = price / gross rent. Illinois transfer tax uses taxable value / $500, rounded up for any fraction, x the applicable rate. Every formula depends on definitions. Identify the correct base, annualize compatible inputs, convert percentages to decimals, carry precision, and obey the stem before calculating.
This is a memory framework for the current exam outline, not a substitute for contracts, loan programs, tax records, disclosure forms, appraisal standards, survey evidence, or legal advice. A supplied problem convention controls its arithmetic. Real commission terms are negotiable. Property-tax rates vary locally. Loan underwriting determines the relevant value and debt. Surveyed acreage can depart from nominal public-land quantities. Operating-expense treatment must match the question. Federal and Illinois source material was checked through August 1, 2026.
How should you memorize real estate math formulas?
- Learn formulas in families: percentage, closing ledger, financing, time proration, measurement, and income valuation.
- Write each parent relationship from memory, then derive its two reverse forms instead of memorizing three disconnected equations.
- Attach plain-language labels to every symbol, including the correct base, period, debt, income level, and requested unknown.
- Pair each formula with one boundary rule, such as loan amount for points, original value for percentage change, or annual NOI for cap rate.
- Practice one clean example and one tempting wrong-base example for every relationship so recognition survives unfamiliar wording.
- Convert units and percentages on separate lines, keeping exact fractions and working precision until the final step.
- Estimate the result, solve, then substitute it into the parent formula or reconcile the ledger to test the arithmetic.
- Review misses by error type: recall, definition, base, unit, posting, rounding, or calculator entry, then repeat the weak family.
- Question family
- Percentage
- Parent formula
- Part = total x decimal rate
- Boundary check
- Name the base
- Question family
- Commission
- Parent formula
- Base x rate
- Boundary check
- Apply splits sequentially
- Question family
- Proration
- Parent formula
- Periodic amount / period x responsible time
- Boundary check
- Use stated convention
- Question family
- LTV
- Parent formula
- Loan / required value
- Boundary check
- Follow included-debt definition
- Question family
- Equity
- Parent formula
- Value - debt
- Boundary check
- Not seller net
- Question family
- Points
- Parent formula
- Loan x points / 100
- Boundary check
- Loan amount base
- Question family
- Area
- Parent formula
- Length x width; triangle / 2
- Boundary check
- Square units
- Question family
- GRM
- Parent formula
- Price / gross rent
- Boundary check
- Match rent period
- Question family
- NOI and cap rate
- Parent formula
- EGI - expenses; NOI / value
- Boundary check
- Annual compatible inputs
- Question family
- Closing
- Parent formula
- Uses - sources; credits - debits
- Boundary check
- Separate party ledgers
Can you follow the calculation from facts to answer?
Derive a missing commission base
Scenario: The total compensation is $19,800 at a stated 5.5% rate. What base produced it?
- Parent relationship is compensation = base x rate.
- Convert 5.5% to 0.055 and divide $19,800 / 0.055.
- The recovered base is $360,000; reverse-check gives $360,000 x 0.055 = $19,800.
Answer: The stated compensation base is $360,000.
Combine LTV and equity without mixing them
Scenario: A property value is $400,000 and the only debt is a $300,000 mortgage. Find LTV and equity.
- LTV = $300,000 / $400,000 = 0.75, or 75%.
- Equity = $400,000 - $300,000 = $100,000.
- The ratio and dollar residual describe related but different quantities.
Answer: LTV is 75%, and equity is $100,000.
Use the correct proration convention
Scenario: A stem supplies $7,300 annual tax, a 365-day method, and 120 seller days. What seller share results?
- Prorated share = annual amount / stated days x responsible days.
- $7,300 / 365 = $20 per day.
- $20 x 120 = $2,400; posting direction depends on whether the item is accrued or prepaid.
Answer: The seller-period share is $2,400 before ledger classification.
Move from income to value
Scenario: Potential income is $110,000, vacancy loss is $5,000, other income is $3,000, operating expenses are $38,000, and cap rate is 8%. Find value.
- Effective gross income is $110,000 - $5,000 + $3,000 = $108,000.
- NOI is $108,000 - $38,000 = $70,000.
- Value = $70,000 / 0.08 = $875,000.
Answer: The indicated value is $875,000.
Calculate an aliquot part
Scenario: What is the nominal acreage in the NE 1/4 of the SW 1/4 of a section?
- Nested fractions multiply: 1 / 4 x 1 / 4 = 1 / 16.
- A nominal section contains 640 acres.
- 640 / 16 = 40 acres.
Answer: The nominal aliquot area is 40 acres.
Apply the Illinois transfer-tax ceiling
Scenario: Using only the stated state rate of $0.50 per $500 or fraction thereof, calculate tax on $250,001 of taxable value.
- $250,001 / $500 = 500.002 statutory units.
- The fraction thereof language raises the count to 501 units.
- 501 x $0.50 = $250.50.
Answer: The stated Illinois state transfer tax is $250.50.
Which math errors cost the most points?
- Trap
- Memorize letters without learning their meanings.
- Correction
- Translate every symbol into the transaction fact before calculating.
- Trap
- Use the largest figure as the percentage base.
- Correction
- Use the base defined by the formula, agreement, program, or stem.
- Trap
- Enter 6 for 6% inside multiplication.
- Correction
- Convert 6% to 0.06.
- Trap
- Apply every commission split to the total fee.
- Correction
- Apply a later split to the subtotal the stem assigns.
- Trap
- Use purchase price for a mortgage-point charge.
- Correction
- One point is 1% of the loan amount.
- Trap
- Call equity the seller's closing proceeds.
- Correction
- Seller net also reflects transaction costs, credits, and prorations.
- Trap
- Use gross rent in the cap-rate formula.
- Correction
- Direct capitalization uses annual NOI, not gross rent.
- Trap
- Use NOI in a gross rent multiplier.
- Correction
- GRM uses consistently defined gross rent and does not deduct expenses.
- Trap
- Assume a universal Illinois property-tax rate.
- Correction
- Aggregate rates depend on local taxing districts and the supplied facts.
- Trap
- Round a transfer-tax unit to nearest.
- Correction
- Raise any partial $500 unit when the rule says fraction thereof.
- Trap
- Treat 640 acres as a surveyed guarantee.
- Correction
- Use it as a nominal exam quantity unless survey facts change the area.
- Trap
- Skip the reverse check after recalling a formula.
- Correction
- Substitute the result or reconcile the ledger to catch setup errors.
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. Which formula finds a percentage amount?
- Part = total x decimal rate
- Part = total / decimal rate
- Rate = total / part
- Total = part x rate
Show answer and explanation
Answer: Part = total x decimal rate
A percentage part is the base or total multiplied by the decimal rate.
2. Which formula finds loan-to-value?
- Loan amount / required value
- Required value / loan amount
- Value - loan amount
- Loan amount x points
Show answer and explanation
Answer: Loan amount / required value
LTV expresses included debt as a share of the applicable value base.
3. Which formula gives value through direct capitalization?
- Annual NOI / decimal cap rate
- Gross rent / cap rate
- Annual NOI x cap rate
- Price / gross rent
Show answer and explanation
Answer: Annual NOI / decimal cap rate
Rearranging rate = NOI / value produces value = NOI / rate.
4. What is the ordinary base for a mortgage-point charge?
- Loan amount
- Purchase price
- Appraised value
- Seller net
Show answer and explanation
Answer: Loan amount
One point equals 1% of the loan amount.
5. What should happen to a partial $500 unit under an Illinois state transfer-tax problem that says 'or fraction thereof'?
- Round the unit up
- Round the unit to nearest
- Discard the fraction
- Convert the unit to percent
Show answer and explanation
Answer: Round the unit up
The statutory wording creates a ceiling rule for any partial unit.
Which numbers and formulas are easy to confuse?
- Terms
- Formula vs. definition
- Difference
- A formula relates quantities. A definition decides which facts qualify for those quantities.
- Question cue
- Correct arithmetic still needs correct inputs.
- Terms
- Rate vs. decimal multiplier
- Difference
- A displayed rate may be 6%. Its multiplier inside arithmetic is 0.06.
- Question cue
- Answer form versus calculator form.
- Terms
- Base vs. largest number
- Difference
- The base is the quantity named by the relationship, not automatically the largest dollar figure.
- Question cue
- Loan amount for points, original value for change.
- Terms
- Gross rent vs. NOI
- Difference
- Gross rent supports GRM. NOI reflects effective income after permitted operating expenses and supports cap rate.
- Question cue
- Before expenses versus after operating expenses.
- Terms
- LTV vs. equity
- Difference
- LTV is debt divided by value. Equity is value minus debt and is expressed as an amount unless converted.
- Question cue
- Ratio versus residual interest.
- Terms
- Seller net vs. equity
- Difference
- Seller net includes transaction credits and debits. Equity is value minus debt before sale costs.
- Question cue
- Closing ledger versus balance relationship.
- Terms
- Proration math vs. posting
- Difference
- The formula finds a share. Accrued or prepaid status determines buyer and seller debit-credit direction.
- Question cue
- Amount first, ledger direction second.
- Terms
- Ordinary rounding vs. ceiling
- Difference
- Ordinary rounding uses place value. A fraction-thereof rule raises any partial statutory unit.
- Question cue
- Nearest versus always upward.
- Terms
- Nominal acreage vs. surveyed acreage
- Difference
- Exam aliquot math often begins with 640 nominal acres, while actual surveyed sections can vary.
- Question cue
- Classroom quantity versus record evidence.
- Terms
- Memorized rule vs. supplied fact
- Difference
- A current general relationship helps with setup, but an explicit stem convention controls the problem.
- Question cue
- Read before recalling.
What does the outline expect you to calculate?
- Topic
- Universal percentage relationship
- What to know
- Part, total, base, rate, percent, decimal, multiplication, division, T-bar, and reverse formula
- Best exam move
- Write part = total x rate and label all three positions before selecting an operation.
- Topic
- Commission and compensation
- What to know
- Sale price, stated base, rate, total fee, firm share, licensee share, referral, sequential percentage, and negotiable term
- Best exam move
- Calculate total compensation first, then apply each stated split to its immediate base.
- Topic
- Property-tax formula
- What to know
- Market value, assessed value, equalization factor, EAV, exemption, taxable EAV, aggregate rate, tax, Cook County, and exceptions
- Best exam move
- Follow the stated assessment sequence and multiply the final taxable base by the decimal aggregate rate.
- Topic
- Proration formula
- What to know
- Annual amount, monthly amount, daily rate, 360 days, 365 days, 366 days, calendar days, responsible days, accrued, and prepaid
- Best exam move
- Divide by the stated period, multiply by responsible time, then assign debit and credit.
- Topic
- Buyer funds
- What to know
- Purchase price, buyer costs, prepaid items, loan proceeds, earnest money, seller credit, proration, debit, credit, and cash needed
- Best exam move
- Add buyer uses and subtract buyer credits and funding once.
- Topic
- Seller net
- What to know
- Sale price, payoff, brokerage compensation, seller cost, transfer tax, credit, proration, debit, credit, proceeds, and shortfall
- Best exam move
- Add seller credits and subtract every distinct seller debit once.
- Topic
- Loan-to-value
- What to know
- Loan amount, value base, price, appraisal, first lien, subordinate debt, LTV, CLTV, HCLTV, maximum loan, and percentage
- Best exam move
- Use LTV = included loan amount / required value and follow the program or stem definition.
- Topic
- Equity
- What to know
- Current value, total debt, mortgage balance, lien, owner interest, sale costs, proceeds, down payment, and change
- Best exam move
- Subtract stated debt from stated value without calling the result cash proceeds.
- Topic
- Mortgage points
- What to know
- Loan amount, one percent, whole point, fractional point, charge, discount point, origination fee, lender credit, and pricing
- Best exam move
- Multiply loan amount by points divided by 100; do not use sale price.
- Topic
- PITI
- What to know
- Principal, interest, property tax, homeowners insurance, mortgage insurance, association dues, monthly amount, annual conversion, and housing expense
- Best exam move
- Add only the components the question includes and convert annual items to monthly once.
- Topic
- Area formulas
- What to know
- Rectangle, square, triangle, irregular shape, length, width, base, height, square feet, and subtraction
- Best exam move
- Sketch, split the shape, calculate each area, and subtract exclusions before converting units.
- Topic
- Acreage and PLSS
- What to know
- 43,560 square feet, acre, section, township, aliquot part, one-half, one-quarter, nominal area, and government survey
- Best exam move
- Multiply denominators for nested aliquot parts and apply the fraction to the nominal section acreage.
- Topic
- Appreciation and depreciation
- What to know
- Original value, new value, dollar change, percentage change, one-period increase, one-period decrease, successive rate, and base
- Best exam move
- Use change / original for the rate or multiply original by 1 plus or minus the decimal rate for one period.
- Topic
- Gross rent multiplier
- What to know
- Sale price, monthly rent, annual rent, gross income, multiplier, comparable, indicated value, unit consistency, and no expenses
- Best exam move
- Use GRM = price / gross rent and match the rent period used to derive the multiplier.
- Topic
- Net operating income
- What to know
- Potential gross income, vacancy loss, collection loss, other income, effective gross income, operating expenses, debt service, depreciation, and capital expenditure
- Best exam move
- Build effective gross income, then subtract the operating expenses allowed by the question.
- Topic
- Capitalization rate
- What to know
- Annual NOI, value, overall rate, income, direct capitalization, decimal rate, inverse relationship, market evidence, and stabilized figures
- Best exam move
- Use rate = NOI / value, value = NOI / rate, or NOI = value x rate with annual inputs.
- Topic
- Illinois transfer tax
- What to know
- Taxable value, $500 unit, fraction thereof, ceiling, state rate, county rate, municipal tax, declaration, exemption, and local variation
- Best exam move
- Divide by $500, raise any fractional unit, and multiply by each applicable supplied rate.
- Topic
- Formula audit
- What to know
- Unknown, units, base, rate, period, definition, estimate, substitute, rounding, and answer sentence
- Best exam move
- Reverse-check the relationship and confirm the result answers the exact unknown.
How should you drill this calculation?
- Session
- Session 1
- Focus
- Write parent formulas
- Proof you are ready
- Reproduce the percentage, closing, financing, proration, measurement, and income relationships from memory twice without notes.
- Session
- Session 2
- Focus
- Derive reverse formulas
- Proof you are ready
- Cover each unknown and derive 30 total, rate, value, loan, rent, and income variations with labeled units.
- Session
- Session 3
- Focus
- Choose bases and periods
- Proof you are ready
- Classify 40 prompts by base, numerator, denominator, time period, and required conversion before solving.
- Session
- Session 4
- Focus
- Mix formula families
- Proof you are ready
- Solve 25 two-stage questions involving tax, splits, closing ledgers, income, financing, or acreage without carrying a subtotal twice.
- Session
- Session 5
- Focus
- Drill boundary rules
- Proof you are ready
- Explain points, NOI, GRM period, LTV value, Illinois transfer-tax ceiling, one-third precision, and nominal acreage aloud.
- Session
- Session 6
- Focus
- Complete a closed-book formula audit
- Proof you are ready
- Score at least 90% on a 40-question mixed set, then sort every miss into recall, definition, base, unit, posting, rounding, or calculator entry and redo it cold.
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 Real Estate Math Formulas to Memorize for the Illinois Exam
Which real estate math formulas should I memorize for the Illinois broker exam?
Know part = total x rate; commission = base x rate; tax = taxable value x rate; proration = periodic amount / stated period x responsible period; LTV = loan / value; points = loan x points / 100; equity = value - debt; area formulas and acreage conversions; GRM = price / gross rent; NOI = effective gross income - operating expenses; cap rate = NOI / value; buyer funds = buyer uses - credits and funding; and seller net = seller credits - seller debits.
Do I need to memorize every variation of each formula?
No. Memorize a small parent formula and rearrange it. From part = total x rate, divide part by rate to recover total or divide part by total to recover rate. From cap rate = NOI / value, recover value with NOI / rate and NOI with value x rate.
What is the most important real estate math formula?
Part = total x decimal rate is the broadest. It supports commission, tax, point charges, down payment, LTV loan amount, vacancy loss, appreciation amount, management fees, and many percentage questions. It does not replace specialized definitions or tell you which number is the correct base.
What conversions should I know without looking them up?
Know 100 cents = $1, 12 inches = 1 foot, 3 feet = 1 yard, 43,560 square feet = 1 acre, 640 acres = 1 section, 36 sections = one standard township, percent / 100 = decimal, and 1 mortgage point = 1% of loan amount. Treat a section and township as nominal survey quantities because real parcels can vary.
What is the formula for commission?
Commission or brokerage compensation = stated compensation base x decimal rate. If a split follows, multiply the total compensation by the stated share, then apply any later split to the new subtotal. Compensation is negotiable, so the problem or agreement must provide the rate and base.
What is the formula for real estate proration?
Prorated share = periodic amount / stated number of days or months x responsible days or months. First identify whether the item is accrued or prepaid, which party owns the closing day, and whether the problem directs a 360-day, 365-day, 366-day, calendar-day, or monthly method.
What are the cap rate, NOI, and GRM formulas?
NOI = effective gross income - operating expenses. Cap rate = annual NOI / value, and value = annual NOI / decimal cap rate. GRM = price / gross rent, and price = gross rent x GRM. Keep gross rent and NOI separate, and match monthly or annual rent to the GRM supplied.
What formulas calculate buyer funds and seller net?
Buyer funds needed = buyer debits or uses - buyer credits and funding sources. Seller net = seller credits - seller debits. Build separate ledgers. Loan proceeds and applied earnest money can reduce buyer cash, while mortgage payoff, compensation, seller-paid costs, credits, and seller obligations reduce seller proceeds.
Should I memorize Illinois tax rates?
Memorize only a current rule the syllabus and source justify, such as the Illinois state transfer-tax rate of $0.50 per $500 or fraction of value. Do not assume one property-tax rate, one local transfer-tax rate, or a universal assessment percentage. Use the figures supplied and respect Cook County, farmland, and preferential-assessment differences.
Are these official Illinois broker exam questions?
No. They are original formula drills aligned to the PSI Illinois broker outline effective June 24, 2026. The outline and primary federal, Illinois, mortgage, and land-survey sources were checked through August 1, 2026.
Primary sources
- PSI Illinois Candidate Information Booklet dated June 24, 2026
- Illinois Department of Revenue, current property-tax assessment and rate guidance
- Illinois Department of Revenue, current real estate transfer-tax rates
- Consumer Financial Protection Bureau, current mortgage points guidance
- Fannie Mae Selling Guide, current LTV ratio definitions
- Consumer Financial Protection Bureau, current Closing Disclosure transaction summaries
- Bureau of Land Management, Manual of Surveying Instructions
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.