Illinois real estate exam math
Calendar-day proration: count the dates, then calculate the share
A one-day counting mistake can change both sides of the closing statement. Start with the period the amount covers and the date each party becomes responsible. Once those facts are clear, the calculation is straightforward.
Last reviewed:
The short answer
For an actual-calendar-year proration, multiply the annual amount by the responsible calendar days, then divide by 365 in a nonleap year or 366 in a leap year. Use that formula when the exercise specifies that convention. A stated fixed-365 or actual/360 method keeps its own denominator. Monthly actual-day rent uses the days in that month. Assign closing day once, keep the daily rate unrounded and determine the debit and credit from who has paid or collected the money.
PSI lists real property tax and other prorations at national XI.A.3. The whole Real Estate Calculations category accounts for 7 of 100 scored national broker questions, without a separate calendar-day quota. These are original practice examples. A real closing follows the contract, applicable law and settlement instructions for dates, estimates and adjustments.
A six-step method for actual-day proration
- Name the amount and its period. An annual charge belongs with an annual basis. A monthly amount belongs with the stated monthly basis. Identify any estimate factor before calculating.
- Write the convention. Actual calendar days describe the count; the instructions also need to establish the denominator. Do not silently replace an expressly stated fixed 365 or actual/360 basis with 366.
- Assign closing day and write both date ranges. If the seller is responsible through closing, the buyer starts the next day. If the buyer is responsible on closing, the seller ends the day before. These are supplied allocations, not universal Illinois defaults.
- Count the responsible dates. Use actual month lengths, including February 29 when present. For a complete shared year, the two parties' days must add to that year's actual 365 or 366 days, even if the specified rate denominator differs.
- Calculate amount x responsible days / matching denominator. Retain the unrounded rate or use the full expression in one calculation. Split the calculation when the instructions require different annual bases or amounts across years.
- Post the adjustment and check it. An unpaid seller-period expense that the buyer will pay calls for a seller debit and buyer credit. A seller-paid expense benefiting the buyer calls for the reverse when reimbursement is required. Rent already collected by the seller needs its own direction.
| Month end | Nonleap year | Leap year |
|---|---|---|
| January | 31 | 31 |
| February | 59 | 60 |
| March | 90 | 91 |
| April | 120 | 121 |
| May | 151 | 152 |
| June | 181 | 182 |
| July | 212 | 213 |
| August | 243 | 244 |
| September | 273 | 274 |
| October | 304 | 305 |
| November | 334 | 335 |
| December | 365 | 366 |
The distinctions that matter
| Distinction | How it works | What to notice |
|---|---|---|
| Actual dates and the rate denominator | Real month lengths determine the calendar-day count. The stated convention determines whether the rate uses 365, 366, 360 or a monthly denominator. | Actual/360 is possible. It is different from a 30-day-month calculation. |
| Annual and monthly amounts | An annual amount divided by annual days gives a daily annual rate. Monthly actual-day rent uses the actual days of its month. | Do not divide one month's rent by 365. |
| Responsible dates and elapsed intervals | A party's inclusive date range counts both endpoints. Simple date subtraction measures the gap between them. | May 1 through May 15 includes 15 dates, not 14. |
| Seller-paid expense and seller-collected rent | An expense paid by the seller may require buyer reimbursement for the buyer's benefit. Rent collected by the seller may require the seller to pass the buyer's share to the buyer. | The word prepaid alone does not establish the direction. Ask who paid whom. |
| Closing estimate and official bill | A contractual proration can use an estimated amount or stated factor. It does not issue a new government tax bill or guarantee the final liability. | A 105% factor must come from the problem or agreement, not an assumed statewide rule. |
| Tenant deposit and earned rent | A security deposit has separate obligations. It is not automatically daily income to divide between owners. | For covered Illinois residential transfers, Section 1.1 also addresses transferee and continuing transferor liability. |
Work through the facts
1. Seller responsible through May 15
The exercise assigns January 1 through May 15, 2026 to the seller. The buyer is responsible May 16 through December 31. Count the days before calculating money.
- 2026 is nonleap. January through April totals 31 + 28 + 31 + 30 = 120 days.
- Include May 1 through 15: 120 + 15 = 135 seller days.
- Buyer days are 365 - 135 = 230. The full-year check is 135 + 230 = 365.
Answer: Seller: 135 days. Buyer: 230 days. Closing day is counted once.
2. Buyer responsible on May 15
Keep the same year and closing date, but give May 15, 2026 to the buyer.
- The seller now ends May 14: 120 + 14 = 134 days.
- The buyer starts May 15: 365 - 134 = 231 days.
- Changing that one instruction moves one day from seller to buyer.
Answer: Seller: 134 days. Buyer: 231 days. The total still equals 365.
3. An accrued tax adjustment
The agreed annual tax estimate is $9,125. Use actual/365 for 2026 and assign the seller 135 days through May 15. No additional factor applies. The buyer will pay the full bill later.
- $9,125 / 365 = $25 per day.
- $25 x 135 = $3,375 for the seller's period.
- The buyer receives an allowance for the seller-period expense the buyer will pay. The remaining year's share is $25 x 230 = $5,750.
Answer: Debit seller and credit buyer $3,375. The $5,750 remainder is the buyer-period share, not a second credit of that amount to the buyer.
4. A full-calendar-year leap basis
For an annual $7,320 charge, the exercise expressly uses actual days over the 366 days of 2028. The seller is responsible January 1 through March 31.
- January 31 + February 29 + March 31 = 91 days.
- $7,320 / 366 = $20 per day; $20 x 91 = $1,820.
- The remaining 275 days account for $5,500. Together the shares equal $7,320.
Answer: The seller-period share is $1,820. Use the payment facts to determine its settlement direction.
5. Rent already collected by the seller
The seller collected all $2,900 rent for February 2028. The agreement gives the buyer rent for February 20 through 29, including the 20th, and requires an adjustment at closing. Use actual days in the month.
- February 2028 has 29 days. The buyer's range contains 10 dates.
- $2,900 / 29 x 10 = $1,000. The seller's 19 dates account for $1,900.
- The seller holds income belonging to the buyer's period. This is different from the seller paying an expense for the buyer.
Answer: Debit seller and credit buyer $1,000 for rent. A separate security deposit is not prorated as rent.
6. An expense paid in advance
The seller paid the $300 June 2026 association charge. The problem requires the buyer to reimburse the seller for June 16 through 30, including both dates, using actual June days.
- June has 30 days; the buyer's period has 15.
- $300 / 30 x 15 = $150.
- Here the seller has paid for the buyer's benefit and is entitled to the stated reimbursement.
Answer: Debit buyer and credit seller $150. Compare that direction with the already-collected rent example.
7. The cost of rounding the daily rate early
An annual $6,500 charge uses a 365-day basis. Allocate 200 days to the seller and 165 to the buyer. Round each final share to cents.
- Keep the full expression: $6,500 x 200 / 365 = $3,561.643835...
- $3,561.64 is the final seller share. Rounding the daily rate to $17.81 first would produce $3,562.00, an error of $0.36.
- The buyer share is $6,500 x 165 / 365 = $2,938.356164..., or $2,938.36. These rounded shares total $6,500.00.
Answer: Use $3,561.64 for the seller-period share. Final-share rounding avoids the amplified daily-rate error.
8. A period crossing December 31
Allocate December 20, 2027 through January 10, 2028, including both endpoints. The instructions use each calendar year's actual denominator. The annual charge is $3,650 for 2027 and $7,320 for 2028.
- December 20 through 31 has 12 days: $3,650 / 365 x 12 = $120.
- January 1 through 10 has 10 days: $7,320 / 366 x 10 = $200.
- Add the two segments: 22 dates and $120 + $200 = $320.
Answer: The share is $320 under the supplied changing annual amounts and bases. One rate for all 22 dates would not follow these instructions.
9. A leap day with an expressly fixed denominator
The annual amount is $3,650. The exercise expressly fixes the denominator at 365 and assigns February 27 through March 1, 2028, including both dates.
- Count February 27, 28 and 29, plus March 1: four actual dates.
- Keep the supplied denominator: $3,650 / 365 x 4 = $40.
- Changing the denominator to 366 would instead give about $39.89. That follows a different convention from the one supplied.
Answer: The requested fixed-365 share is $40. The calendar count includes February 29 even though the denominator remains 365.
10. A stated estimate factor
The last annual bill is $9,000. A simplified exercise directs a 105% estimate, 100 seller days and a 365-day basis. The buyer will pay the estimated full bill later.
- Apply the instructed factor: $9,000 x 1.05 = $9,450.
- Calculate without intermediate rounding: $9,450 x 100 / 365 = $2,589.041095...
- Applying 1.05 to the unrounded share gives the same result. Rounding an intermediate amount can change it.
Answer: Debit seller and credit buyer $2,589.04 under these assumptions. Neither 105% nor this estimate is a universal Illinois legal requirement.
Mistakes to avoid
- Giving closing day to both parties or neither party Write adjacent date ranges and check that the same full year totals 365 or 366 actual days.
- Always choosing 366 when February 29 appears Count the leap day, then use the expressly stated denominator.
- Assuming actual/360 means thirty days in every month Actual/360 retains real calendar days. A 30/360 method uses its own month assumptions and endpoint rules.
- Dividing monthly rent by an annual denominator Match the period of the amount to the stated monthly calculation.
- Reversing all prepaid entries the same way Separate a seller-paid expense from rent a tenant paid to the seller.
- Rounding the daily rate to cents before multiplication Keep precision through the share calculation. Follow any explicit rounding instruction.
- Treating an estimate factor or closing-day choice as Illinois law Use the exercise or agreement. IDOR's general guidance leaves the allocation to contract terms.
- Prorating the security deposit as daily rent Handle its separate balance and applicable obligations. A closing credit alone does not establish that all statutory liability ends.
Check your understanding
These are original teaching questions, not recalled or predicted PSI questions. Answer first, then explain why the other choices fail.
1. How many dates are included from January 1 through March 31, 2026?
- 90
- 91
- 89
- 120
Show answer and explanation
Answer: A. 90
January 31 + February 28 + March 31 = 90. The 89 count omits a date; 91 fits the corresponding 2028 leap-year range; 120 reaches April 30, 2026. Both endpoints belong to this stated range.
2. Closing is May 15, 2026, and the buyer is responsible on closing day. How many seller days run from January 1?
- 231
- 133
- 135
- 134
Show answer and explanation
Answer: D. 134
The seller ends May 14: 31 + 28 + 31 + 30 + 14 = 134. The 135 count gives May 15 to the seller; 133 omits another date. The 231 figure is the buyer's complementary full-year count, not the seller's.
3. An annual $9,125 estimate uses actual/365. The seller is assigned 135 days, and no other factor applies. What is the seller-period amount?
- $3,421.88
- $3,350
- $5,750
- $3,375
Show answer and explanation
Answer: D. $3,375
$9,125 / 365 x 135 = $3,375. The $3,350 choice uses 134 days; $5,750 is the 230-day complement; $3,421.88 is the rounded result of replacing 365 with 360. Keep the instructed amount, count and basis together.
4. The buyer will later pay the full unpaid tax bill. Which paired adjustment allocates the seller's accrued share?
- Debit both parties
- Credit both parties
- Credit seller and debit buyer
- Debit seller and credit buyer
Show answer and explanation
Answer: D. Debit seller and credit buyer
The buyer receives an allowance for the seller-period expense. Reverse entries would reimburse a seller who had already paid an applicable buyer-period expense, a different situation. Two debits or two credits do not supply the paired adjustment described.
5. Which year is a Gregorian leap year?
- 1900
- 2100
- 2026
- 2000
Show answer and explanation
Answer: D. 2000
2000 is divisible by 400. The century years 1900 and 2100 are not; 2026 is not divisible by 4. Apply the century exception before adding a leap day.
6. The seller collected February 2028 rent of $2,900. The buyer is entitled to February 20 through 29, inclusive, with a closing adjustment. Use actual monthly days. Which entry fits?
- Seller debit and buyer credit $100
- Buyer debit and seller credit $1,000
- Seller debit and buyer credit $900
- Seller debit and buyer credit $1,000
Show answer and explanation
Answer: D. Seller debit and buyer credit $1,000
The buyer is entitled to ten of February's 29 dates: $2,900 / 29 x 10 = $1,000. The seller holds the buyer-period rent, so the seller is debited. The reverse direction confuses rent collected with a seller-paid expense; $900 omits a buyer date; $100 covers only one date.
7. The seller paid a $300 June charge. The buyer must reimburse June 16 through 30, inclusive, on actual June days. What is the adjustment?
- Buyer debit and seller credit $140
- Buyer debit and seller credit $150
- Seller debit and buyer credit $150
- Buyer debit and seller credit $300
Show answer and explanation
Answer: B. Buyer debit and seller credit $150
June 16 through 30 has 15 dates, so $300 / 30 x 15 = $150. The buyer reimburses an expense the seller paid for the buyer's period. The reversed direction confuses this with collected rent; $140 omits one date; $300 charges the buyer for the entire month.
8. Allocate 200 days of an annual $6,500 amount using a 365-day denominator. Keep precision until the final cents. Which share is correct?
- $3,561.64
- $2,938.36
- $3,551.91
- $3,562.00
Show answer and explanation
Answer: A. $3,561.64
The calculation is $6,500 x 200 / 365 = $3,561.643835..., rounded to $3,561.64. The $3,562.00 choice rounds the daily rate early; $3,551.91 uses a 366-day denominator; $2,938.36 is the 165-day complement on the stated basis. The final shares here reconcile to $6,500.
9. Use each year's actual denominator for December 20, 2027 through January 10, 2028, inclusive. Annual amounts are $3,650 for 2027 and $7,320 for 2028. What share follows?
- $320
- $220
- $440
- $300
Show answer and explanation
Answer: A. $320
Twelve December dates at $3,650 / 365 = $10 produce $120. Ten January dates at $7,320 / 366 = $20 produce $200. The total is $320. The $220 and $440 choices apply only one segment's rate to all 22 dates; $300 does not allocate all the supplied dates at their specified rates.
10. For February 27 through March 1, 2028, inclusive, the exercise expressly fixes a 365-day denominator for an annual $3,650 amount. What is the share?
- $40.56
- $40
- $39.89
- $30
Show answer and explanation
Answer: B. $40
The four dates are February 27, 28, 29 and March 1. The specified calculation is $3,650 / 365 x 4 = $40. The $30 omits one date; $39.89 changes the basis to 366; $40.56 changes it to 360. Count actual dates while retaining the stated denominator.
11. A $9,000 annual bill is estimated at an instructed 105%. Allocate 100 days on a 365-day basis without intermediate rounding. What is the final share?
- $2,589.04
- $2,589.00
- $2,500.00
- $2,465.75
Show answer and explanation
Answer: A. $2,589.04
$9,000 x 1.05 x 100 / 365 = $2,589.041095..., or $2,589.04. The $2,465.75 omits the factor; $2,500 uses the unfactored amount and 360 basis; $2,589 rounds an intermediate daily rate. The 105% factor is supplied, not a statewide legal default.
12. A problem supplies the amount, year and day-count basis but never assigns closing day. What is the best next step?
- Identify the missing allocation or state a conditional assumption
- Always assign it to the seller under an assumed statewide rule
- Give closing day to both parties
- Omit closing day from both shares
Show answer and explanation
Answer: A. Identify the missing allocation or state a conditional assumption
The missing allocation can move a day's charge between parties. Ask for the instruction or clearly qualify an illustrative assumption. Double counting, omitting the date and inventing a universal Illinois default do not resolve the missing fact.
Common questions
What is the calendar-day proration formula?
Use full-period amount x responsible actual days / the matching stated denominator. For an actual-calendar-year amount, that denominator is 365 or 366. For actual monthly rent, it is the number of days in that month. A specifically instructed fixed-365 or actual/360 basis retains its own denominator.
Does the seller or buyer get closing day in Illinois?
Use the contract or exercise instructions. Seller through closing assigns that date to the seller; buyer on closing assigns it to the buyer. IDOR's general closing guidance refers to the real estate contract. Do not invent a statewide allocation when the relevant instruction is missing.
How do I use the cumulative-day table?
Add the date in the closing month to the previous month's cumulative total when the seller is responsible through that date. For May 15, 2026, April ends at 120 and the inclusive count is 135. If the buyer is responsible on May 15, end the seller count at May 14 for 134 days. This January 1 start must match the problem.
Which years are leap years?
In the Gregorian calendar, a year divisible by 4 is a leap year unless it is a century year not divisible by 400. Thus 2028 and 2000 are leap years; 2026 and 2100 are not. February has 29 days in a leap year, and the full calendar year has 366.
Should I always divide by 366 in a leap year?
No. Use 366 for the actual-calendar-year convention described here. If the question expressly supplies a fixed-365 or actual/360 basis, retain it while counting the actual assigned dates, including February 29. The numerator and denominator are separate choices.
Is actual/360 the same as 30/360?
No. Fannie Mae's cited interest guidance distinguishes actual calendar days with a 360 denominator from a 30-day-month method with a 360 denominator. That lending-program example demonstrates the difference. It does not establish a default Illinois tax-proration convention, and a 30 / 360 exercise may also need endpoint rules.
How do I prorate monthly rent by actual days?
Divide the month's amount by its actual days, then multiply by the assigned dates. For February 2028, $2,900 / 29 x 10 = $1,000. A 31-day month uses 31 under that method. Do not substitute an annual denominator or treat a separate tenant security deposit as rent.
When do I debit the seller and credit the buyer?
For an accrued seller-period expense the buyer will pay later, the buyer receives the seller's share. The same direction can apply to buyer-period rent already collected by the seller. Identify both the responsible period and who currently holds or owes the money before posting the pair.
Why does a seller-paid expense reverse the rent entry?
If the seller already paid an expense that benefits the buyer and the agreement requires reimbursement, debit the buyer and credit the seller for that benefit. If a tenant paid buyer-period rent to the seller, the seller instead owes that income to the buyer. The word prepaid alone is not enough to choose direction.
Should a tenant security deposit be prorated by ownership days?
Do not automatically treat it as daily earned rent. It is a separate balance subject to applicable duties. For the residential transfers covered by 765 ILCS 710 / 1.1, the transferee is liable for the tenant's deposit, statutory interest or prepaid rent, and the transferor remains jointly and severally liable. A closing allocation does not by itself end every legal obligation.
Does Illinois require a 105% tax-proration factor?
The cited IDOR guidance does not prescribe a universal 105% factor. Use a factor when the exercise or agreement supplies it. Apply it without intermediate rounding and label the result an estimate. Actual closing terms may also provide for reproration after the bill arrives.
Why can the Illinois tax year differ from the payment year?
IDOR describes a general two-year cycle: valuation occurs in the first year, then bills are calculated and mailed in the second. Count the period the tax amount actually covers. A bill's payment date alone does not make it a charge for that same calendar year.
What if separately rounded shares differ by a penny?
Keep the full rate through each calculation, then follow the final rounding and reconciliation instructions. For example, $1,000.01 split equally across two 183-day periods of a 366-day year gives $500.005 each. Rounding each share to the nearest cent with a half cent rounded up gives $500.01 twice, totaling $1,000.02. Follow the settlement instructions for the balancing penny. Do not change a day count to force agreement.
How do I calculate a period that crosses December 31?
Identify the method and amounts before splitting. When the instructions use each year's actual annual basis, calculate each segment using that year's amount and 365 or 366 days, then add the shares. A fixed contractual rate or a single defined billing period can require a different treatment. Do not assume every cross-year problem has the same formula.
Keep practising
Your next practice step
Put real estate math into practice
Set up the calculation, keep the units consistent, and check the worked answer.
These web resources are free. The app has a separate free starter tier and optional paid full access.
Official sources and scope
The official sources establish the exam topic, calendar rule, general Illinois tax context and specified disclosure or tenant-balance duties. The dates, amounts and allocation instructions in the examples are original assumptions. No example supplies a statewide closing-day default, a universal tax estimate factor or a live tax bill.
- PSI June 24, 2026: real property tax and other prorations
- IDOR: property-tax responsibility at closing
- IDOR: the general two-year property-tax cycle
- CFPB Regulation Z 1026.38: paired closing adjustments and rent
- Fannie Mae: actual/360 and 30/360 interest methods
- U.S. Naval Observatory: the Gregorian leap-year rule
- 765 ILCS 710/1.1: covered residential transfers and tenant balances
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.