Illinois real estate math guide
Illinois property tax math and prorations
First decide whether the question asks for a tax bill or a closing adjustment. A bill starts with the taxable value and rate. A proration starts with the amount to allocate, the dates and who will pay. Keeping those two calculations separate makes the rest much easier.
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The short answer
For a simplified Illinois tax bill, apply the stated assessment level to market value, multiply by the applicable equalization factor, subtract qualifying EAV exemptions and multiply the remaining taxable EAV by the decimal aggregate tax rate. If the question already gives taxable EAV, start there. For a proration, multiply the annual proration base by the responsible days divided by the stated year denominator. Follow the stated day-count and closing-day rules. When the buyer will pay unpaid taxes for the seller's period, that adjustment is a seller debit and buyer credit.
Reviewed October 24, 2026. Real property tax and other prorations appear at National XI.A.3 in the June 24, 2026 PSI broker outline. The whole Real Estate Calculations area is seven of 100 scored national questions, not a quota for this page. The examples are simplified, with their assessment levels, rates, exemptions and contract conventions supplied. Actual Illinois bills and closings require the applicable law, county records and contract.
Choose the base before you calculate
- Name the unknown. Is it assessed value, gross EAV, taxable EAV, a tax bill, a rate, exemption savings or a party's closing adjustment? Do not repeat assessment or subtract an exemption twice when the question already gives the final taxable value.
- Build the value chain only as far as needed. Most Illinois property is assessed at one-third of market value, but Cook County classification and special property categories require different treatment. Use the supplied assessment level. Apply the appropriate equalization factor to assessed value before subtracting the qualifying EAV exemptions in the simplified problem.
- Identify how the rate is quoted. Illinois rates are generally expressed as dollars per $100 of equalized assessed valuation, equivalent to a percentage. A rate of $7.50 per $100 is 7.5%, or 0.075. A multiplier of 1.08 is already a factor; do not convert it to 0.0108. Add supplied applicable district rates only when the problem has not already given their aggregate.
- Use the correct exemption effect. An EAV exemption reduces the base, rather than subtracting that many dollars from the bill. With the rate held fixed, tax savings equal the EAV reduction multiplied by the decimal rate. An eligibility condition or statutory maximum is not an instruction to give every owner that amount. That fixed-rate arithmetic is not a promise about a later year's bill, when the rate, value or exemptions may change.
- For a proration, establish the annual base. The contract may require the known annual bill, 105% of the prior bill or another estimate. Build that base before allocating days. A contractual estimate is not a new tax rate or an official determination of the next bill.
- Write both day-count instructions. Identify the year denominator and how days are counted. If the question says 30/360, use the specified 30-day months and 360-day year. If it says actual/365 or actual/actual, use its calendar and denominator. Mark who receives closing day. A 360 denominator alone does not tell you to replace every actual month with 30 days.
- Set the direction from payment status. For unpaid seller-period taxes that the buyer will pay, reduce the seller's proceeds and credit the buyer. For taxes already paid by the seller that benefit the buyer's period, reimburse the seller: seller credit and buyer debit. A buyer's lender escrow deposit is a separate entry, not a second credit for the same seller liability.
- Keep precision and check the result. Retain intermediate digits unless the question supplies a rounded daily amount or another rounding instruction. Round the final dollar result as requested. Check units, percentage conversion, day totals and opposite ledger entries; an adjustment is counted once on each party's statement.
| Find | Calculation | Check before using it |
|---|---|---|
| Assessed value | Market value x stated assessment level | Use one-third only when appropriate or supplied. |
| Gross EAV | Assessed value x applicable equalization factor | Do not apply the factor again to supplied EAV. |
| Taxable EAV | Gross EAV - qualifying EAV exemptions | Subtract only deductions not already included. |
| Annual tax | Taxable EAV x decimal aggregate rate | 7.5% = 0.075. |
| Aggregate rate | Annual tax / taxable EAV | Multiply the decimal by 100 to express percent. |
| Taxable EAV from tax | Annual tax / decimal aggregate rate | This is not automatically market value. |
| Effective rate | Annual tax / full market value | Different denominator from the aggregate rate. |
| Exemption savings | EAV reduction x decimal rate | Hold the rate fixed in the simplified problem. |
| Rate in mills | Mills / 1,000 | A national unit conversion, not a different assessment rule. |
| Party proration | Annual proration base x responsible days / stated year days | Use the given month and closing-day conventions. |
The distinctions that matter
| Distinction | How it works | What to notice |
|---|---|---|
| Market value vs. assessed value | Market value is the full-value starting point in a conventional assessment problem. Assessed value applies the stated assessment level. Cook residential property does not use the general one-third shortcut. | Do not apply a tax rate to the wrong value. |
| Assessed value vs. gross EAV | The applicable equalization factor adjusts assessed value. This guide calls the result before homestead deductions gross EAV, then calls the remaining base taxable EAV. | Identify which stage the supplied number represents. |
| EAV exemption vs. dollar tax credit | An EAV reduction is multiplied by the tax rate to find its simplified tax effect. A dollar credit, when applicable, adjusts a calculated tax liability directly. | A $6,000 EAV reduction at 7% saves $420, not $6,000. |
| Aggregate rate vs. effective tax rate | The aggregate rate is applied to taxable EAV. The effective rate compares the tax bill with full market value. They use different denominators. | Ask what value sits beneath the division sign. |
| Annual bill vs. installment | An installment is a payment toward a tax-year bill. Under an accelerated billing system, the first installment can be based on the prior bill; it need not equal half the new annual tax. | Do not automatically double the first payment. |
| Assessment year vs. payment year | Illinois generally values property in the first year and calculates and bills the tax in the second. A 2026 payment can relate to the 2025 assessment year. | Read the year covered, rather than only the due date. |
| Unpaid allocation vs. prepaid reimbursement | The direction changes with who paid and whose period benefited. The word tax, by itself, does not choose the debit or credit. | Identify the payer and the ownership period first. |
| Property tax vs. transfer tax | Annual property-tax math uses the taxable property base and local rates. Transfer-tax math concerns a taxable conveyance and its applicable consideration units. | A stamp rate is not an annual property-tax rate. |
Work through the facts
Work the complete value chain
A simplified problem gives $360,000 market value, a one-third assessment level, a 1.08 equalization factor, a qualifying $8,000 EAV exemption and a 7.5% aggregate rate.
- $360,000 x 1/3 = $120,000 assessed value.
- $120,000 x 1.08 = $129,600 gross EAV.
- $129,600 - $8,000 = $121,600 taxable EAV.
- $121,600 x 0.075 = $9,120 annual tax.
Answer: $9,120. The $8,000 deduction reduced EAV, not the tax bill directly.
Start with taxable EAV when it is already supplied
The problem states that taxable EAV, after all qualifying exemptions, is $100,000. The aggregate rate is $7.50 per $100.
- $7.50 / $100 = 0.075.
- $100,000 x 0.075 = $7,500.
- Do not divide the stated taxable EAV by three or subtract another exemption.
Answer: The annual tax is $7,500.
Compare aggregate and effective rates
A parcel has $96,000 taxable EAV, $320,000 full market value and a $7,680 annual tax bill.
- Aggregate rate: $7,680 / $96,000 = 0.08 = 8%.
- Effective rate: $7,680 / $320,000 = 0.024 = 2.4%.
- Both calculations are consistent because they use different bases.
Answer: 8% of taxable EAV and 2.4% of market value describe the same stated bill.
Find the tax effect of an exemption
A qualifying EAV exemption is $6,000. Hold the stated aggregate rate at 8.25%.
- 8.25% = 0.0825.
- $6,000 x 0.0825 = $495.
- This is a fixed-rate comparison, not a prediction that local rates stay unchanged in a later tax year.
Answer: The simplified bill decreases by $495.
Convert mills without importing another state's assessment rules
A national math question supplies $120,000 taxable value and a 24-mill rate.
- One mill is $1 per $1,000 of taxable value, or 0.001.
- 24 mills = 0.024 = 2.4%.
- $120,000 x 0.024 = $2,880.
Answer: The tax is $2,880. Use the supplied taxable base; do not substitute another jurisdiction's assessment percentage.
Count actual days to a June closing
The 2026 annual proration base is $7,300. Use actual calendar days and a 365-day year. Closing is June 15, assigned to the buyer; the seller is charged January 1 through June 14. The buyer will pay this unpaid tax.
- Seller days: 31 + 28 + 31 + 30 + 31 + 14 = 165.
- $7,300 x 165 / 365 = $3,300.
- Buyer days: 365 - 165 = 200; $7,300 x 200 / 365 = $4,000.
- The shares total $7,300.
- If the question assigned June 15 to the seller instead, the share would include one more $20 day, producing $3,320.
Answer: Record the $3,300 seller-period adjustment as a seller debit and buyer credit. Do not also charge the buyer the seller's period a second time.
Build a 105% estimate before prorating
The contract requires 105% of the prior $7,200 annual bill, a 360-day year and 100 seller days.
- $7,200 x 1.05 = $7,560 annual proration base.
- $7,560 / 360 = $21 per stated day.
- $21 x 100 = $2,100.
Answer: The seller's estimated allocation is $2,100. The contract, not a statewide 105% rule, supplied that percentage.
Reimburse a prepaid buyer-period benefit
The seller has already paid tax covering 40 days allocated to the buyer. The problem supplies an applicable daily amount of $18.50.
- 40 x $18.50 = $740.
- The buyer received the benefit of the seller's payment.
- Reimbursement increases seller proceeds and the buyer's funds needed by the same amount.
Answer: $740 seller credit and $740 buyer debit.
Use a leap-year denominator when instructed
A 2028 actual/actual problem uses 366 days, a $7,320 annual base and a March 1 closing assigned to the buyer. The seller is responsible for January 1 through February 29.
- 31 + 29 = 60 seller days.
- $7,320 / 366 = $20 per day.
- $20 x 60 = $1,200.
Answer: The seller allocation is $1,200 under the stated actual/actual convention.
See why early daily rounding changes the result
Allocate a $10,000 annual base over 137 days in a 365-day problem. The question asks for the final share to the nearest cent and supplies no rounded daily rate.
- $10,000 x 137 / 365 = $3,753.424657...
- Rounding the final amount gives $3,753.42.
- Rounding the daily rate first to $27.40 gives $3,753.80, which is $0.38 higher.
Answer: Use $3,753.42 for this question. If a different question expressly supplies $27.40 as the daily amount, use that supplied input instead.
Mistakes to avoid
- The current sale price is always the taxable value. Identify market value, assessed value and taxable EAV separately. A bill can cover an earlier assessment year.
- An equalization factor of 1.08 means multiply by 0.0108. 1.08 is already the stated multiplier. Convert the tax percentage separately.
- Every Illinois home uses the same assessment percentage and tax rate. Cook classification, special property methods and local taxing-district rates prevent that shortcut.
- The statutory exemption maximum is a flat credit against every bill. Check eligibility and the qualifying EAV reduction. Apply the rate to the reduced base.
- A 360-day denominator necessarily gives a complete month-count rule. Read the supplied convention. State 30/360 when using 30-day months; actual/360 would use a different numerator.
- The seller always gets closing day. Follow the question or contract. One extra day changes the allocated amount.
- Illinois law universally requires a 105% estimate. Use the contractual percentage or other basis stated. Do not create one.
- Unpaid seller taxes are a seller credit. If the buyer will pay the seller-period amount, it is a seller debit and buyer credit.
- The first installment always equals half the annual bill. Accelerated billing can use a prior-year basis. Verify the annual amount and covered period.
- A tax cap freezes each owner's bill. PTELL limits qualifying taxing-district extensions; it does not cap every individual assessment or bill.
Check your understanding
These are original teaching questions, not recalled or predicted PSI questions. Answer first, then explain why the other choices fail.
1. Gross EAV is $110,000, the qualifying EAV exemption is $10,000 and the aggregate rate is 8%. What is the simplified annual tax?
- $7,200
- $8,800
- $8,000
- $100,000
Show answer and explanation
Answer: C. $8,000
$110,000 - $10,000 = $100,000 taxable EAV. Multiply by 0.08 to obtain $8,000. $8,800 ignores the exemption; $100,000 is the value base, not the tax.
2. Taxable EAV after exemptions is $100,000. The rate is $7.50 per $100. What is the tax?
- $33,333.33
- $750,000
- $750
- $7,500
Show answer and explanation
Answer: D. $7,500
$7.50 per $100 equals 7.5%, or 0.075. $100,000 x 0.075 = $7,500. The supplied value is already taxable EAV; do not apply an assessment level again.
3. A $6,000 EAV exemption applies at a fixed 7% aggregate rate. What is its simplified tax effect?
- $857.14 decrease
- $6,000 decrease
- $42 decrease
- $420 decrease
Show answer and explanation
Answer: D. $420 decrease
$6,000 x 0.07 = $420. An EAV exemption reduces the base, not the bill dollar for dollar. This comparison holds the rate fixed.
4. Annual tax is $7,680 and the decimal aggregate rate is 0.08. What taxable EAV is implied?
- $768,000
- $9,600
- $96,000
- $614.40
Show answer and explanation
Answer: C. $96,000
$7,680 / 0.08 = $96,000. Check: $96,000 x 0.08 = $7,680. This recovers taxable EAV, not necessarily gross EAV or market value.
5. A national calculation gives $120,000 taxable value and 24 mills. What is the tax?
- $2,880
- $288
- $5,000
- $28,800
Show answer and explanation
Answer: A. $2,880
24 mills = 24 / 1,000 = 0.024. $120,000 x 0.024 = $2,880. A mill is not one percentage point, and the question already supplies the taxable base.
6. Use actual/365 for 2026 and a $7,300 annual base. June 15 closing belongs to the buyer. The seller covers January 1 through June 14. What is the seller share?
- $3,320
- $3,300
- $4,000
- $3,280
Show answer and explanation
Answer: B. $3,300
Actual seller days are 31 + 28 + 31 + 30 + 31 + 14 = 165. $7,300 x 165 / 365 = $3,300. $3,320 includes closing day; $3,280 substitutes 30-day months; $4,000 is the buyer-period share.
7. The buyer will pay an unpaid tax bill that includes the seller's $2,500 accrued share. Which adjustment allocates that seller share?
- $2,500 debit to both parties
- $2,500 seller credit and buyer debit
- $2,500 credit to both parties
- $2,500 seller debit and buyer credit
Show answer and explanation
Answer: D. $2,500 seller debit and buyer credit
The seller owes the allocated period but the buyer will pay the bill. Reduce seller proceeds and credit the buyer by $2,500. This is the same adjustment shown on opposite ledgers, not two separate charges.
8. The seller already paid taxes that benefit 40 buyer days. A daily amount of $18.50 is supplied. What is the reimbursement?
- $740 seller debit and buyer credit
- $400 seller credit and buyer debit
- $18.50 seller credit and buyer debit
- $740 seller credit and buyer debit
Show answer and explanation
Answer: D. $740 seller credit and buyer debit
40 x $18.50 = $740. The buyer reimburses the seller for the prepaid buyer-period benefit. This reverses the unpaid seller-period adjustment.
9. A contract specifies 105% of the last $7,200 bill, a 360-day year and 100 seller days. What is the seller allocation?
- $2,000
- $7,560
- $200
- $2,100
Show answer and explanation
Answer: D. $2,100
First calculate $7,200 x 1.05 = $7,560. Then $7,560 x 100 / 360 = $2,100. $2,000 ignores the percentage; $7,560 is the full annual estimate.
10. A question supplies no rounded daily rate and asks for $10,000 x 137 / 365 to the nearest cent. Which amount fits?
- $3,753.42
- $2,740.00
- $3,750.00
- $3,753.80
Show answer and explanation
Answer: A. $3,753.42
The unrounded result is $3,753.424657..., so the final amount is $3,753.42. $3,753.80 results from prematurely rounding the daily rate to $27.40. Follow a different question's explicit supplied daily rate if it gives one.
Common questions
How do you calculate an Illinois property-tax bill?
In a simplified problem, taxable EAV multiplied by the decimal aggregate rate gives the annual tax. If you start with market value, first apply the stated assessment level, applicable equalization factor and qualifying EAV exemptions. Stop repeating steps once the question has already supplied their result.
What is EAV, and why distinguish gross from taxable EAV?
EAV means equalized assessed value. In the usual problem, assessed value is multiplied by the applicable equalization factor. This guide uses gross EAV for the value before qualifying homestead deductions and taxable EAV for the remaining tax base. Read whether a supplied number is before or after exemptions; terminology on a bill or question can be abbreviated.
Does all Illinois property use a one-third assessment level?
No. IDOR says most property does, but Cook County uses classification, including 10% for residential property and 25% for commercial property. Farmland and other specially treated property need separate methods. Use the actual property category and the level supplied by the question.
Is an 8% aggregate rate the same as an 8% effective rate?
No. The aggregate rate is applied to taxable EAV. The effective rate divides the tax bill by full market value. For example, $7,680 / $96,000 taxable EAV is 8%, while $7,680 / $320,000 market value is 2.4%.
How do rates per $100 and mills convert to decimals?
$7.50 per $100 is 7.5%, or 0.075. One mill is $1 per $1,000 of taxable value, or 0.001, so 24 mills is 0.024. The unit changes the conversion; it does not change the question's supplied assessment or taxable base.
Does a homestead exemption reduce the bill dollar for dollar?
An EAV exemption reduces taxable value. With the rate held fixed, an $8,000 EAV reduction at 7.5% reduces the simplified bill by $600. The actual qualifying exemption and rate must be established; a statutory maximum is not automatic eligibility or a flat dollar credit.
What are the current General Homestead Exemption maximums?
Section 15-175 states maximum EAV reductions of $10,000 in counties with at least 3,000,000 inhabitants, $8,000 in contiguous counties and $6,000 in other counties for taxable years 2023 and thereafter. IDOR identifies these as Cook, counties contiguous to Cook and the remaining counties. Eligibility and the statutory calculation still apply. Use the qualifying amount in the problem rather than assuming every owner receives the maximum. The ordinary statutory calculation relates the current EAV to the 1977 base, subject to the stated maximum and statutory exceptions; the maximum is a ceiling, not an extra amount added to that increase.
Does a seller's exemption automatically become the buyer's future exemption?
Do not assume that the prior bill predicts the new owner's eligibility, exemptions or final future bill. Check the particular exemption and local assessment office requirements. A closing estimate based on the seller's old bill is a contractual allocation, not a guarantee that the next bill will match it.
Does a property-tax cap freeze every individual bill?
No. IDOR explains that PTELL limits growth in qualifying taxing-district extensions; it does not cap each individual property assessment or bill. The assessment, exemptions, applicable rates and other statutory provisions still matter.
How do you calculate a closing proration?
Establish the annual base, identify the day-count method and year denominator, count the allocated days and calculate annual base x allocated days / year days. Then assign the debit and credit from payment status. A numeric share alone does not identify the correct ledger direction.
Must Illinois prorations always use 360 days or charge closing day to the seller?
No universal convention is supplied by those labels. Follow the contract or explicit exam instructions. State both the numerator convention, such as actual days or 30-day months, and the denominator. If a necessary convention is missing, identify the missing fact instead of quietly inventing it. For actual/actual in a leap year, a 366-day denominator may be specified; do not silently replace the problem's stated denominator.
Is 105% a mandatory Illinois tax-proration percentage?
No universal 105% requirement is established by the guidance used here. IDOR ties the parties' closing responsibility to their real estate contract. Use 100%, 105%, 110% or another estimate only when the question or contract supplies it, and check any reproration agreement.
When are taxes a seller debit and buyer credit?
When the adjustment covers the seller's unpaid accrued share and the buyer will pay the bill, the seller's proceeds decrease and the buyer receives a credit. If the seller instead prepaid a benefit for the buyer's period, reimbursement is a seller credit and buyer debit. Lender reserves are separate.
Why does the payment year matter?
Illinois generally uses a two-year cycle: the assessment relates to the first year, with billing and payment in the second. Identify the actual tax year, installment, payment status and period being allocated. Do not assume a bill paid in 2026 assesses 2026 ownership or that every first installment equals half the annual tax.
Should I round the daily rate before multiplying?
Keep intermediate precision unless the problem supplies a rounded daily amount or another instruction. Round the final result as requested. The rounding example shows a $0.38 difference from an early daily-rate rounding step; that is a calculation result, not a special PSI rounding rule.
Can I use the transfer-tax rate for this calculation?
No. Annual property tax uses the taxable value and applicable local rates. Transfer tax is a separate conveyance calculation using its own consideration basis and units. Choose the calculation from what the question asks.
Are these official exam questions or a validated readiness test?
No. These ten original questions are teaching exercises aligned with the cited topic. They do not reproduce PSI material or show that a particular practice percentage predicts passing. Review the base, units, date count and ledger reasoning for every answer.
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Official sources and scope
Reviewed October 24, 2026. The January 2026 Illinois property-tax guide, current IDOR answers and relevant Section 15-175 text support the Illinois explanations. Relevant first-party indexed statutory text was used where direct ILGA access failed. Publication 136 is dated April 2016 and reformatted in 2019; it supplies general definitions, not current exemption limits. The Michigan Legislature reference supplies only the mill unit, not Michigan assessment percentages or tax limits. All example amounts and contract conventions are stated assumptions, with arithmetic checked independently. No current county bill, individual exemption eligibility or settlement entitlement is determined here. The General Homestead Exemption amounts come from the enacted provision; proposed changes are not treated as law.
- PSI Illinois booklet, June 24, 2026: National XI.A.3
- IDOR: assessment levels, local rates and installment methods
- IDOR: seller tax responsibility, contracts and reproration
- IDOR PTAX-1004, January 2026: value chain, extension and tax bills
- IDOR Publication 136, April 2016: assessment and equalization definitions
- IDOR: current homestead exemption and PTELL explanation
- 35 ILCS 200/15-175: General Homestead Exemption limits and conditions
- Michigan Legislature, For the People, page 33: mill definition only
- IDOR: real estate transfer tax definition, separate from annual property tax
This is exam preparation, not advice for a specific transaction. State law and the applicable facts control. Our editorial and corrections process explains how to report an issue.