- Official section
- National XI.C: Prorations for Tax and Other Items
- Broker weight
- A core skill within 7% of the national portion
- Expected scored items
- The current PSI broker outline assigns about 7 of 100 scored national items to Real Estate Math
Illinois real estate math guide
Illinois property tax math and prorations
A property tax problem usually asks one of two questions. What is the bill, or which party carries part of it at closing? Build the value chain for the first and a dated ledger for the second. Mixing EAV math with proration math is the fastest way to lose an otherwise easy point.
Last updated: August 1, 2026
What calculation do you need to make?
Short answer: For a simplified Illinois bill, fair market value times the stated assessment level gives assessed value. Assessed value times the equalization factor gives gross EAV. Subtract qualifying EAV exemptions to get taxable EAV. Taxable EAV times the decimal aggregate tax rate gives the property tax. To prorate a known annual amount, divide by the stated 360-day or 365-day year and multiply by the responsible days. For a calendar method, count the actual days in each month. A seller credit for unpaid accrued tax is a seller debit and buyer credit. Illinois has no single statewide property tax rate, exemptions do not reduce the bill dollar for dollar, and transfer tax is a separate calculation.
This guide uses simplified exam formulas. Actual Illinois bills reflect local assessments, classification where applicable, equalization, exemptions, taxing-district levies and rates, PTELL and statutory limits where applicable, corrections, appeals, and county administration. Closing entries follow the contract, bill status, title practice, lender requirements, and any reproration agreement. Use the numbers and day-count convention stated in the question. Sources were checked through August 1, 2026.
How do you solve Illinois property tax math?
- Box the requested result: assessed value, EAV, taxable EAV, annual tax, rate, exemption savings, daily rate, or proration.
- For a tax bill, write the value chain in order: market value, assessment level, equalization factor, exemptions, and aggregate rate.
- Convert every percentage to a decimal and keep the equalization factor separate because it is already a multiplier.
- Subtract qualifying EAV exemptions from gross EAV before applying the property tax rate.
- For a proration, establish the annual base and the required 360-day, 365-day, leap-year, or calendar convention.
- Mark whether the closing day belongs to the buyer or seller, then count responsible days visibly.
- Assign the result by payment status: unpaid accrued expense or prepaid benefit, with opposite buyer and seller entries.
- Reverse-check the arithmetic and reject any result that confuses property tax, transfer tax, EAV, or a dollar credit.
- Unknown
- Assessed value
- Formula
- Market value x assessment level
- Exam safeguard
- Use stated level
- Unknown
- Gross EAV
- Formula
- Assessed value x equalization factor
- Exam safeguard
- Factor is not tax rate
- Unknown
- Taxable EAV
- Formula
- Gross EAV - qualifying EAV exemptions
- Exam safeguard
- Do not subtract from tax
- Unknown
- Annual property tax
- Formula
- Taxable EAV x decimal aggregate rate
- Exam safeguard
- No statewide rate
- Unknown
- Aggregate rate
- Formula
- Annual tax / taxable EAV
- Exam safeguard
- Convert decimal to percent
- Unknown
- Taxable EAV from bill
- Formula
- Annual tax / decimal rate
- Exam safeguard
- Multiply back to verify
- Unknown
- Exemption tax effect
- Formula
- EAV reduction x decimal rate
- Exam safeguard
- Not dollar for dollar
- Unknown
- Daily tax rate
- Formula
- Annual proration base / stated days
- Exam safeguard
- Use 360, 365, or 366
- Unknown
- Party proration
- Formula
- Daily rate x responsible days
- Exam safeguard
- Check closing-day rule
- Unknown
- Unpaid seller period
- Formula
- Seller debit and buyer credit
- Exam safeguard
- Count once on each ledger
Can you follow the calculation from facts to answer?
Build the full Illinois tax value chain
Scenario: A problem gives a $360,000 market value, a 33 1/3% assessment level, a 1.08 equalization factor, a qualifying $8,000 EAV exemption, and a 7.5% aggregate rate. What is the simplified annual tax?
- Assessed value is $360,000 x 1/3 = $120,000.
- Gross EAV is $120,000 x 1.08 = $129,600; taxable EAV is $129,600 - $8,000 = $121,600.
- Annual tax is $121,600 x 0.075 = $9,120.
Answer: The simplified annual property tax is $9,120.
Calculate the effect of an EAV exemption
Scenario: A qualifying exemption reduces EAV by $6,000 and the aggregate tax rate is 8.25%. How much does the simplified bill decrease?
- The exemption removes $6,000 from the taxable base.
- Convert 8.25% to 0.0825.
- $6,000 x 0.0825 = $495, not $6,000.
Answer: The simplified tax reduction is $495.
Recover the aggregate property tax rate
Scenario: A parcel has taxable EAV of $96,000 and an annual tax bill of $7,680. What aggregate rate does the simplified problem imply?
- $7,680 / $96,000 = 0.08.
- Convert 0.08 to 8%.
- Check: $96,000 x 0.08 = $7,680.
Answer: The aggregate rate is 8%.
Prorate taxes with a 365-day year
Scenario: Annual taxes are $8,760. The problem uses 365 days and charges the seller with 150 days. What is the seller's accrued share?
- Daily tax is $8,760 / 365 = $24.
- The seller share is $24 x 150 = $3,600.
- If the tax is unpaid, that amount is a seller debit and buyer credit.
Answer: The seller's share is $3,600.
Use an estimated proration base
Scenario: The contract tells you to prorate at 105% of the last $7,200 tax bill. Using a 360-day year and 100 seller days, what is the seller share?
- The annual proration base is $7,200 x 1.05 = $7,560.
- The daily rate is $7,560 / 360 = $21.
- The seller share is $21 x 100 = $2,100.
Answer: The contract-based seller proration is $2,100.
Reverse a prepaid-tax adjustment
Scenario: The seller already paid a tax installment that covers 40 buyer days after closing. The applicable daily amount is $18.50. How is the adjustment entered?
- The buyer-period benefit is 40 x $18.50 = $740.
- Because the seller prepaid the buyer's period, the buyer reimburses the seller.
- The adjustment raises seller proceeds and buyer cash needed by the same amount.
Answer: Enter a $740 seller credit and $740 buyer debit.
Which math errors cost the most points?
- Trap
- Multiply full market value by the tax rate in every Illinois problem.
- Correction
- Illinois bills generally use taxable EAV, which follows assessment, equalization, and qualifying exemptions.
- Trap
- Use 33 1/3% for every parcel in Illinois.
- Correction
- Cook County classification and special property categories require different treatment; use the supplied assessment level.
- Trap
- Treat the equalization factor as a percentage tax rate.
- Correction
- The factor adjusts assessed value; the aggregate rate is applied later to taxable EAV.
- Trap
- Subtract an $8,000 EAV exemption directly from the tax bill.
- Correction
- Subtract it from EAV, then multiply the remaining taxable EAV by the rate.
- Trap
- Assume Illinois has one statewide property tax rate.
- Correction
- The aggregate rate depends on the taxing districts serving the parcel.
- Trap
- Use the transfer-tax rate to estimate annual property tax.
- Correction
- Transfer tax uses consideration units; property tax uses taxable EAV and local rates.
- Trap
- Default to 360 days without reading the question.
- Correction
- Use the stated 360-day, 365-day, leap-year, or actual-calendar convention.
- Trap
- Automatically charge the closing day to the seller.
- Correction
- Follow the contract or exam direction and make the inclusion choice explicit.
- Trap
- Prorate the last bill when the problem requires 105% of it.
- Correction
- Adjust the annual base first, then calculate the daily and party shares.
- Trap
- Give the seller a credit for unpaid accrued taxes.
- Correction
- When the buyer will pay that future bill, the seller's accrued share is generally a seller debit and buyer credit.
- Trap
- Call a proration the final tax liability in every closing.
- Correction
- An estimate can be subject to the contract and later reproration when the actual bill arrives.
- Trap
- Round the daily rate too early.
- Correction
- Keep full precision until the final amount unless the problem supplies a rounded daily rate.
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 parcel has $110,000 gross EAV, a $10,000 qualifying EAV exemption, and an 8% aggregate rate. What is the simplified annual tax?
- $8,000
- $8,800
- $7,200
- $10,000
Show answer and explanation
Answer: $8,000
Taxable EAV is $100,000, and $100,000 x 0.08 = $8,000.
2. A $6,000 EAV exemption applies where the aggregate rate is 7%. How much does the simplified tax bill decrease?
- $420
- $6,000
- $857.14
- $42
Show answer and explanation
Answer: $420
$6,000 x 0.07 = $420.
3. Annual taxes are $7,300. Using 365 days and 90 seller days, what is the seller share?
- $1,800
- $2,000
- $1,825
- $657
Show answer and explanation
Answer: $1,800
$7,300 / 365 = $20 per day, and $20 x 90 = $1,800.
4. The seller prepaid an expense covering the buyer's post-closing period. What is the normal proration direction?
- Seller credit and buyer debit
- Seller debit and buyer credit
- Debit both parties
- Credit both parties
Show answer and explanation
Answer: Seller credit and buyer debit
The buyer reimburses the seller for a benefit the seller already paid.
5. Which statement about Illinois property tax rates is correct?
- There is no single statewide property tax rate
- Every county uses exactly 8%
- The transfer-tax rate controls the annual bill
- Every parcel is taxed directly on sale price
Show answer and explanation
Answer: There is no single statewide property tax rate
Applicable local taxing-district rates and the parcel's taxable EAV drive the bill.
Which numbers and formulas are easy to confuse?
- Terms
- Market value vs. assessed value
- Difference
- Market value estimates the property's full fair cash value. Assessed value applies the legally relevant assessment level to that value.
- Question cue
- Full value versus assessment percentage value.
- Terms
- Assessed value vs. EAV
- Difference
- Assessed value is the assessor-level result. EAV applies the state equalization factor to that assessed value.
- Question cue
- Before multiplier versus after multiplier.
- Terms
- Gross EAV vs. taxable EAV
- Difference
- Gross EAV is the equalized value before exemptions. Taxable EAV is the remaining base after qualifying EAV exemptions.
- Question cue
- Before exemptions versus after exemptions.
- Terms
- EAV exemption vs. tax credit
- Difference
- An EAV exemption reduces the value multiplied by the rate. A tax credit directly reduces a calculated tax liability when applicable.
- Question cue
- Base reduction versus dollar reduction.
- Terms
- Individual district rate vs. aggregate rate
- Difference
- An individual rate funds one taxing district. The aggregate rate combines the applicable district rates for the parcel.
- Question cue
- One levy rate versus combined parcel rate.
- Terms
- Property tax vs. transfer tax
- Difference
- Property tax recurs and uses taxable EAV. Transfer tax arises from a taxable conveyance and uses consideration units.
- Question cue
- Annual ownership charge versus conveyance charge.
- Terms
- Tax bill vs. proration base
- Difference
- The tax bill is an assessed amount. A contract may use that bill, a percentage of it, or another estimate as the closing proration base.
- Question cue
- Official amount versus settlement estimate.
- Terms
- Unpaid tax vs. prepaid tax
- Difference
- Unpaid accrued tax creates a seller debit and buyer credit for the seller period. Prepaid tax benefiting the buyer can reverse those entries.
- Question cue
- Future payer reimbursement versus prior payer reimbursement.
- Terms
- 360-day method vs. calendar method
- Difference
- The 360-day method treats every month as 30 days. The calendar method uses actual month lengths and the stated annual denominator.
- Question cue
- Standardized months versus actual dates.
- Terms
- Assessment year vs. payment date
- Difference
- The tax relates to a tax year, while installments can be billed or paid later. Closing math must identify which period the bill covers.
- Question cue
- Liability period versus due date.
What does the outline expect you to calculate?
- Topic
- Fair market value
- What to know
- Fair cash value, market value, appraisal, sale price, assessment date, mass appraisal, arm's-length transaction, improvement, land, building, parcel, and tax year
- Best exam move
- Treat market value as the starting value only when the problem asks you to build assessed value from it.
- Topic
- Assessment level
- What to know
- Assessment percentage, 33 1/3%, decimal conversion, one-third, county, classification, Cook County, residential class, farmland, preferential assessment, and supplied rate
- Best exam move
- Multiply by the level stated in the problem and do not force the one-third shortcut onto every parcel.
- Topic
- Assessed value
- What to know
- Market value, assessment level, assessed valuation, assessor, township, county, quadrennial assessment, reassessment, new construction, and taxable parcel
- Best exam move
- Calculate assessed value as market value times the stated assessment level before applying equalization.
- Topic
- Equalization factor
- What to know
- State multiplier, county assessment level, Department of Revenue, factor above one, factor below one, aggregate assessment, uniformity, assessed value, and multiplication
- Best exam move
- Multiply assessed value by the exact factor supplied; a factor is not a tax rate.
- Topic
- Gross EAV
- What to know
- Equalized assessed value, assessed value, equalization factor, gross value, parcel, exemption base, tax-rate base, abbreviation EAV, and calculation sequence
- Best exam move
- Finish equalization before subtracting any EAV exemption stated in the question.
- Topic
- EAV exemptions
- What to know
- General Homestead Exemption, Senior Citizens Homestead Exemption, returning veterans, disabled veterans, disabled persons, home improvement, eligibility, application, maximum reduction, county category, and tax year
- Best exam move
- Subtract only qualifying exemptions supplied by the problem and recognize that most are value reductions, not dollar tax credits.
- Topic
- General Homestead maximums
- What to know
- Taxable year 2023 and after, $10,000, county with 3,000,000 or more inhabitants, $8,000, contiguous county, $6,000, other county, increase in EAV, maximum reduction, and eligibility
- Best exam move
- Treat the statutory amount as a maximum EAV reduction and still use the actual qualifying amount stated or calculated.
- Topic
- Taxable EAV
- What to know
- Gross EAV, qualifying exemption, net EAV, taxable value, subtraction, nonnegative result, parcel, taxing district, and bill base
- Best exam move
- Subtract EAV exemptions before multiplying by the aggregate rate.
- Topic
- Aggregate tax rate
- What to know
- County, municipality, school district, park district, library district, fire district, levy, individual district rate, combined rate, percentage, decimal, and local variation
- Best exam move
- Add district rates only if the problem requires it, then convert the aggregate percentage to a decimal once.
- Topic
- Tax bill formula
- What to know
- Taxable EAV, aggregate rate, annual property tax, multiplication, dollar result, local rate, extension, tax bill, installment, and estimate
- Best exam move
- Multiply taxable EAV by the decimal aggregate rate and label the result as annual tax unless told otherwise.
- Topic
- Reverse tax formulas
- What to know
- Known tax, unknown rate, known EAV, unknown EAV, division, decimal rate, percentage conversion, base, check, and reasonableness
- Best exam move
- Rate equals tax divided by taxable EAV; taxable EAV equals tax divided by the decimal rate.
- Topic
- Mill conversion
- What to know
- Mill, one-thousandth, $1 per $1,000, decimal 0.001, mills to decimal, mills to dollars, assessed value, national terminology, and local rate format
- Best exam move
- Use one mill as 0.001 and do not confuse a mill with one percentage point.
- Topic
- Known bill proration
- What to know
- Annual tax bill, prior bill, estimated bill, contractual percentage, 100%, 105%, 110%, annual base, seller days, buyer days, and reproration
- Best exam move
- Build the annual proration base exactly as the problem directs before finding a daily rate.
- Topic
- 360-day method
- What to know
- Statutory year, banker's year, 12 months, 30 days per month, annual amount, daily rate, month count, day count, closing date, and instruction
- Best exam move
- Divide by 360 and count every month as 30 days only when the problem specifies that method.
- Topic
- 365-day method
- What to know
- Calendar year denominator, 365, leap year, 366, annual amount, daily rate, elapsed days, responsible days, and closing allocation
- Best exam move
- Use the supplied denominator and count the ownership period without silently assigning the closing day.
- Topic
- Calendar-day method
- What to know
- January 31, February 28 or 29, April 30, actual days, closing day, beginning date, ending date, cumulative day count, and inclusive count
- Best exam move
- Write month totals before adding the partial month so an off-by-one error becomes visible.
- Topic
- Closing debit and credit
- What to know
- Seller ownership period, unpaid tax, accrued tax, seller debit, buyer credit, prepaid tax, seller credit, buyer debit, outstanding bill, escrow, and settlement statement
- Best exam move
- Decide who paid and who benefited before assigning the same proration to opposite sides of the ledger.
- Topic
- Property tax versus transfer tax
- What to know
- Recurring tax, transaction tax, EAV, aggregate rate, consideration, revenue stamp, $500 unit, state rate, county rate, annual bill, and closing charge
- Best exam move
- Use EAV for property tax and stated consideration units for transfer tax; the formulas are unrelated.
How should you drill this calculation?
- Session
- Session 1
- Focus
- Build the Illinois value chain
- Proof you are ready
- Solve ten market-value, assessment-level, equalization-factor, and EAV problems in the correct order.
- Session
- Session 2
- Focus
- Master exemptions and rates
- Proof you are ready
- Calculate taxable EAV, aggregate tax, exemption savings, missing rates, and missing taxable values in 20 problems.
- Session
- Session 3
- Focus
- Count ownership days
- Proof you are ready
- Count seller and buyer days for 15 closings under explicit closing-day and leap-year rules.
- Session
- Session 4
- Focus
- Use every proration method
- Proof you are ready
- Solve ten 360-day, ten 365-day, and ten calendar-method property tax prorations.
- Session
- Session 5
- Focus
- Assign debits and credits
- Proof you are ready
- Classify 20 unpaid, prepaid, estimated, escrowed, and reprorated tax adjustments on both ledgers.
- Session
- Session 6
- Focus
- Complete a mixed property tax set
- Proof you are ready
- Score at least 90% and justify each answer by value base, rate, exemption, day method, closing-day rule, payer, and ledger direction.
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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Drill this topic, then review the explanation
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Questions students ask about Illinois Property Tax Math and Proration Examples
How do you calculate an Illinois property tax bill?
For a simplified exam problem, multiply the property's taxable equalized assessed value by the decimal aggregate tax rate. Taxable EAV is gross EAV after the qualifying exemptions stated in the problem. If taxable EAV is $120,000 and the aggregate rate is 8%, the tax is $9,600.
What is equalized assessed value in Illinois?
Equalized assessed value, or EAV, is assessed value multiplied by the applicable state equalization factor. After qualifying homestead exemptions are removed, the resulting taxable value is used with the applicable taxing-district rates to calculate the bill.
Is Illinois property assessed at one-third of market value?
Most property is assessed at 33 1/3% of fair market value, but that is not a universal shortcut. Cook County uses classification with different assessment levels, farmland and some other property use special methods, and the problem may provide a different assessment level. Use the facts given.
Does Illinois have one statewide property tax rate?
No. Illinois property taxes depend on EAV and the rates for the local taxing districts serving the property. For an exam calculation, use the aggregate rate supplied by the question and do not import a rate from another county or municipality.
How does a homestead exemption affect Illinois property tax?
An EAV exemption reduces taxable EAV, not the tax bill dollar for dollar. If an exemption reduces EAV by $8,000 and the aggregate rate is 7.5%, the simplified tax reduction is $8,000 times 0.075, or $600. Eligibility and maximums depend on the particular exemption and county category.
How do you calculate a property tax proration?
Divide the annual tax amount by the number of days required by the problem, then multiply by the number of responsible days. Under a 365-day method, $7,300 produces a $20 daily rate. If the seller owns 125 charged days, the seller share is $2,500.
Is the closing day charged to the buyer or seller?
Follow the contract or exam instruction. If the seller owns through the day before closing, exclude closing day from seller days. If the problem says the seller owns the closing day, include it. Never decide by habit when the prompt states the convention.
Why is the Illinois seller often credited or debited for taxes at closing?
For an existing home, IDOR explains that the seller generally pays outstanding bills and provides a credit to the buyer for the seller's ownership period, according to the contract. The buyer generally handles bills due after closing. The exact settlement entry depends on the contract, bill status, estimate, and reproration agreement.
Is property tax the same as Illinois transfer tax?
No. Property tax is a recurring local tax tied to taxable EAV and taxing-district rates. Transfer tax is a transaction charge calculated from taxable consideration in stated units. Do not use the Illinois transfer-tax rate to calculate an annual property tax bill.
Are these official Illinois broker exam questions?
No. They are original calculations aligned to the PSI broker outline effective June 24, 2026. PSI, the Illinois Property Tax Code, and current Illinois Department of Revenue guidance were checked through August 1, 2026.
Primary sources
- PSI Illinois Candidate Information Booklet dated June 24, 2026
- Illinois Department of Revenue, current property assessment levels and local tax-rate explanation
- Illinois Department of Revenue, current seller property-tax responsibility at closing
- Illinois Department of Revenue, current property taxpayer information
- Illinois Department of Revenue, FY 2026 Property Tax Study
- Illinois Department of Revenue Publication 136, current Property Assessment and Equalization
- 35 ILCS 200/15-175, current General Homestead Exemption
- 35 ILCS 200, current Illinois Property Tax Code
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.