- Official section
- National XI.B: Tax and Other Prorations
- Broker weight
- A named real estate math skill within the national outline
- Expected scored items
- The current PSI broker outline assigns about 7 of 100 scored national items to Real Estate Math
Actual-day proration guide
Count the calendar period exactly once
Actual-day proration is a date problem before it is a money problem. Write who owns closing day, mark the first and last responsible dates, and count real month lengths. Once the count is stable, divide the full-period amount by the matching actual-day denominator and multiply. If you use a cumulative day number, ask whether that numbered date belongs to the party. Including the date uses its day number; ending the day before usually subtracts one.
Last updated: August 1, 2026
What calculation do you need to make?
Short answer: For an annual calendar-day proration, daily rate equals annual amount divided by 365 in a nonleap year or 366 in a leap year when that convention is stated. Multiply the unrounded daily rate by the party's actual responsible calendar days. Determine closing-day ownership before counting. In a nonleap year, month-end cumulative totals are 31, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334, and 365; add one from February onward in a leap year. For a monthly actual-day item, divide by the actual days in that month rather than the annual denominator. A period crossing December 31 may require separate yearly or billing-period segments when leap status or the annual amount changes. After finding the share, identify whether the item is accrued, prepaid, collected, or held and assign balanced debits and credits. Count the period a second way and round the final money result, not the daily rate, unless instructed otherwise.
Calendar-day examples are simplified exam exercises. Actual contracts and settlement instructions determine closing-day ownership, applicable period, tax factor, estimated bill, reproration, prepaid-item treatment, and payer allocation. Illinois property taxes are generally handled through an in-arrears cycle, but a particular closing can use negotiated estimates and adjustments. Rent, association charges, utilities, interest, and insurance can have different billing periods and governing documents. A tenant security deposit is not automatically earned rent and may transfer as a held liability under separate legal duties. Federal disclosure rules address presentation for covered loans without dictating every substantive allocation. This page is exam preparation, not legal, tax, property-management, or closing advice. Sources were checked through August 1, 2026.
How do you calculate an actual calendar-day proration?
- Identify the full-period amount, billing period, due status, requested party, and requested settlement entry.
- Confirm the year, leap status, actual-day convention, and which party owns or benefits on closing day.
- Write the responsible start and end dates and count actual days month by month or through cumulative day numbers.
- Divide an annual amount by 365 or 366, or divide a monthly amount by that month's actual number of days.
- Multiply the unrounded daily rate by the responsible days and round only the final amount as instructed.
- Identify accrued, prepaid, collected, or held status before deciding seller and buyer debit-credit direction.
- Count the other party's period independently or use a valid full-period complement to confirm no missing or duplicated calendar day remains.
- State the amount, party, entry, date convention, and any estimated or simplified qualifier in the final answer at closing.
- Task
- Nonleap daily rate
- Formula or rule
- Annual amount / 365
- Exam safeguard
- Actual days
- Task
- Leap-year daily rate
- Formula or rule
- Annual amount / 366
- Exam safeguard
- Only when directed
- Task
- Monthly daily rate
- Formula or rule
- Monthly amount / days in month
- Exam safeguard
- 28, 29, 30, or 31
- Task
- Seller owns through closing
- Formula or rule
- Include closing date
- Exam safeguard
- Buyer starts next day
- Task
- Buyer owns on closing
- Formula or rule
- Seller ends prior day
- Exam safeguard
- Buyer includes closing
- Task
- Seller share
- Formula or rule
- Daily rate x seller days
- Exam safeguard
- Unrounded rate
- Task
- Buyer full-year days
- Formula or rule
- Year days - seller days
- Exam safeguard
- Same full period
- Task
- Accrued seller tax
- Formula or rule
- Seller debit, buyer credit
- Exam safeguard
- Buyer later pays
- Task
- Prepaid seller benefit
- Formula or rule
- Seller credit, buyer debit
- Exam safeguard
- Buyer benefits later
- Task
- Full-year check
- Formula or rule
- Seller days + buyer days = 365 or 366
- Exam safeguard
- One closing day
Can you follow the calculation from facts to answer?
Count a seller period through closing
Scenario: A nonleap-year closing is May 15, and the seller owns through closing. How many seller days run from January 1?
- Month-end cumulative days through April equal 120.
- Include May 1 through 15: 120 + 15 = 135.
- Buyer begins May 16 under the stated convention.
Answer: The seller has 135 actual calendar days.
Give closing day to the buyer
Scenario: A nonleap-year closing is May 15, and the buyer owns on closing day. How many seller days run from January 1?
- The seller's final day is May 14.
- Cumulative days through April are 120, plus 14 May days.
- 120 + 14 = 134.
Answer: The seller has 134 actual calendar days.
Calculate an accrued tax share
Scenario: Annual estimated tax is $9,125 in a nonleap year. Seller owns through May 15, a 135-day period, and buyer will later pay the bill.
- $9,125 / 365 = $25 per day.
- $25 x 135 = $3,375.
- Because tax is accrued and buyer pays later, debit seller and credit buyer.
Answer: Debit seller and credit buyer $3,375.
Use leap-year actual days
Scenario: A leap-year problem expressly uses 366 days. Annual dues are $7,320 and the responsible period is 91 days. What is the share?
- $7,320 / 366 = $20 per day.
- $20 x 91 = $1,820.
- The 366 denominator matches the stated leap-year convention.
Answer: The prorated share is $1,820.
Prorate February rent by actual month days
Scenario: February rent is $2,900 in a leap year. The buyer is entitled to 10 actual February days. What rent share applies?
- Leap-year February has 29 days.
- $2,900 / 29 = $100 per day.
- $100 x 10 = $1,000.
Answer: The buyer-period rent share is $1,000.
Preserve daily-rate precision
Scenario: An annual charge is $6,500 in a nonleap year, and the seller period is 200 days. What is the actual-day share?
- $6,500 / 365 = $17.80821918 per day before rounding.
- $17.80821918 x 200 = $3,561.643836.
- Round the final amount to $3,561.64.
Answer: The seller's actual-day share is $3,561.64.
Which math errors cost the most points?
- Trap
- Use 30 days for every month in an actual-day problem.
- Correction
- Use the real length of each calendar month.
- Trap
- Forget February's leap day.
- Correction
- Confirm the year before using February and the annual denominator.
- Trap
- Count elapsed intervals instead of responsible dates.
- Correction
- Apply the stated inclusive or exclusive closing-day allocation.
- Trap
- Give closing day to both seller and buyer.
- Correction
- Assign the date exactly once.
- Trap
- Give closing day to neither party.
- Correction
- Reconcile the two counts to the full intended period.
- Trap
- Divide monthly rent by 365.
- Correction
- Use the actual days in the stated monthly billing period.
- Trap
- Divide an annual charge by days in the closing month.
- Correction
- Use the annual 365 or 366 denominator for an annual actual-day item.
- Trap
- Round a repeating daily rate to cents first.
- Correction
- Carry precision through multiplication and round the final money result.
- Trap
- Treat a tenant security deposit as prepaid rent.
- Correction
- A deposit is held subject to separate obligations and is not automatically earned income.
- Trap
- Post an accrued seller tax as a seller credit.
- Correction
- When buyer pays later, seller is debited and buyer is credited for seller's share.
- Trap
- Use full-year subtraction across different billing periods.
- Correction
- The complement works only when both shares cover the same complete period.
- Trap
- Call the estimate the final tax obligation.
- Correction
- A contractual closing allocation does not replace the later official bill or agreed reproration.
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. In a nonleap year, how many calendar days run from January 1 through March 31?
- 90 days
- 89 days
- 91 days
- 120 days
Show answer and explanation
Answer: 90 days
January 31 + February 28 + March 31 = 90.
2. A nonleap-year closing is April 10 and seller owns through closing. How many seller days run from January 1?
- 100 days
- 99 days
- 101 days
- 90 days
Show answer and explanation
Answer: 100 days
Days through March total 90, plus 10 April days.
3. A leap-year annual charge is $7,320. What daily rate applies under an expressly stated 366-day method?
- $20
- $20.05
- $610
- $24
Show answer and explanation
Answer: $20
$7,320 / 366 = $20 per day.
4. Monthly rent is $3,100 for a 31-day month. What is the actual daily rate?
- $100
- $103.33
- $8.49
- $101.92
Show answer and explanation
Answer: $100
$3,100 / 31 = $100 per day.
5. Buyer will later pay an accrued unpaid tax for the seller's ownership period. What entry applies?
- Debit seller and credit buyer
- Credit seller and debit buyer
- Debit both parties
- Credit both parties
Show answer and explanation
Answer: Debit seller and credit buyer
The buyer receives a credit for the seller-period obligation the buyer will later pay.
Which numbers and formulas are easy to confuse?
- Terms
- Calendar-day vs. 30-day-month method
- Difference
- Calendar-day uses actual month lengths. A 30-day method assigns every month 30 days under its convention.
- Question cue
- Real calendar versus assumed month.
- Terms
- Annual actual-day vs. monthly actual-day
- Difference
- Annual uses 365 or 366. Monthly uses the actual number of days in the billing month.
- Question cue
- Year denominator versus month denominator.
- Terms
- Inclusive vs. exclusive closing day
- Difference
- Inclusive gives closing day to seller. Exclusive ends seller responsibility the day before.
- Question cue
- Seller through closing versus buyer on closing.
- Terms
- Elapsed intervals vs. responsible days
- Difference
- Date subtraction counts intervals between dates. Proration counts the calendar dates assigned to a party.
- Question cue
- Time gap versus ownership count.
- Terms
- Nonleap vs. leap year
- Difference
- Nonleap has 365 days and February 28. Leap has 366 days and February 29.
- Question cue
- Ordinary February versus added day.
- Terms
- Accrued vs. prepaid item
- Difference
- Accrued is incurred but unpaid. Prepaid is paid before all benefit has been received.
- Question cue
- Payment later versus payment already made.
- Terms
- Rent vs. security deposit
- Difference
- Rent is payment for occupancy. A security deposit remains subject to separate duties and is not automatically earned income.
- Question cue
- Income versus tenant-held obligation.
- Terms
- Party share vs. debit-credit entry
- Difference
- The share measures the responsible amount. The entry records settlement direction between parties.
- Question cue
- Amount versus posting.
- Terms
- Daily-rate rounding vs. final rounding
- Difference
- Daily-rate rounding can amplify error. Final rounding preserves precision across the responsible days.
- Question cue
- Early shortcut versus accurate finish.
- Terms
- Estimated tax proration vs. tax bill
- Difference
- A proration allocates an estimated or known amount by agreement. The tax bill is issued through the taxing process.
- Question cue
- Closing adjustment versus government liability.
What does the outline expect you to calculate?
- Topic
- Actual-day method
- What to know
- Calendar days, annual amount, daily rate, 365, 366, nonleap year, leap year, actual month length, responsible period, and multiplication
- Best exam move
- Use real calendar days and the matching denominator supplied by the problem.
- Topic
- Full-period amount
- What to know
- Annual tax, annual insurance, yearly association fee, monthly rent, monthly utility, billing cycle, known bill, estimate, and stated base
- Best exam move
- Match the denominator to the full period represented by the amount.
- Topic
- Nonleap year
- What to know
- 365 days, February 28, January 31, month lengths, annual denominator, cumulative totals, and calendar check
- Best exam move
- Use 365 and 28 February days when the stated year is nonleap.
- Topic
- Leap year
- What to know
- 366 days, February 29, divisibility, century exception, annual denominator, cumulative totals, and date confirmation
- Best exam move
- Use 366 only when the year and stated actual-day convention require it.
- Topic
- Month lengths
- What to know
- January 31, February 28 or 29, March 31, April 30, May 31, June 30, July 31, August 31, September 30, October 31, November 30, December 31
- Best exam move
- Write month lengths rather than relying on an unverified mental count.
- Topic
- Cumulative day table
- What to know
- Day of year, month-end total, prior months, add current day, subtract one, seller day number, buyer start, and cross-check
- Best exam move
- Use the prior month-end cumulative total plus the current month's date number when that date is included.
- Topic
- Seller owns through closing
- What to know
- Inclusive closing day, seller end date, buyer starts next day, day-of-year number, accrued share, prepaid share, and contract convention
- Best exam move
- Include the closing date in seller days exactly once.
- Topic
- Buyer owns on closing
- What to know
- Seller ends prior day, buyer begins closing day, exclusive seller count, one-day difference, responsibility, and settlement instruction
- Best exam move
- Subtract one from the inclusive closing day number to find seller days from January 1.
- Topic
- Seller-day count
- What to know
- January 1 start, month-by-month sum, closing date, prior day, inclusive range, actual days, and stated ownership
- Best exam move
- Write the date range and total each month before calculating money.
- Topic
- Buyer-day count
- What to know
- Closing day or next day, year end, remaining days, total year minus seller days, direct count, no gap, and no overlap
- Best exam move
- Confirm seller days plus buyer days equal 365 or 366 for a full-year allocation.
- Topic
- Partial monthly period
- What to know
- Monthly rent, actual month denominator, daily rent, closing date, days remaining, days elapsed, 28, 29, 30, 31, and benefit
- Best exam move
- Divide by that month's actual days when the problem uses a monthly actual-day method.
- Topic
- Cross-year period
- What to know
- Start year, end year, December, January, leap status, separate denominators, billing period, full days, and calendar sequence
- Best exam move
- Split the period by year or billing cycle when one denominator does not describe the entire span.
- Topic
- Accrued property tax
- What to know
- Seller ownership, unpaid bill, paid in arrears, buyer later pays, seller debit, buyer credit, annual estimate, and closing
- Best exam move
- Allocate the seller's accrued share and post the balanced entry stated by the problem.
- Topic
- Prepaid rent or charge
- What to know
- Advance payment, rent collected, tenant, buyer ownership, seller receipt, unearned period, seller debit, buyer credit, and assignment
- Best exam move
- Credit the party entitled to the post-closing benefit or income under the stated facts.
- Topic
- Security deposit distinction
- What to know
- Tenant funds, transfer, credit, liability, rent distinction, escrow, ownership change, statutory duty, and settlement entry
- Best exam move
- Do not prorate a deposit as earned rent merely because both appear in the lease ledger.
- Topic
- Daily-rate precision
- What to know
- Annual division, repeating decimal, calculator memory, intermediate digits, cents, final rounding, cumulative error, and proof
- Best exam move
- Keep the unrounded daily rate through multiplication.
- Topic
- Debit-credit direction
- What to know
- Buyer debit, buyer credit, seller debit, seller credit, amount, accrued, prepaid, payer, beneficiary, and balanced entry
- Best exam move
- Decide direction after identifying payment status and responsibility.
- Topic
- Calendar verification
- What to know
- Second count, cumulative total, direct month sum, complement, full-year reconciliation, closing day, leap check, unit, and reasonableness
- Best exam move
- Verify the day count independently before accepting the money result.
How should you drill this calculation?
- Session
- Session 1
- Focus
- Memorize and verify month lengths
- Proof you are ready
- Write all month lengths and nonleap cumulative month-end totals from memory, then check them.
- Session
- Session 2
- Focus
- Count seller days
- Proof you are ready
- Count 25 periods under seller-through-closing and buyer-on-closing conventions.
- Session
- Session 3
- Focus
- Handle leap years and monthly periods
- Proof you are ready
- Solve 20 leap-year annual and 20 actual-month rent or charge prorations.
- Session
- Session 4
- Focus
- Calculate annual shares
- Proof you are ready
- Solve 25 actual-day annual prorations while preserving daily-rate precision.
- Session
- Session 5
- Focus
- Assign entries and verify counts
- Proof you are ready
- Post 30 accrued, prepaid, rent, and deposit scenarios and reconcile both party periods.
- Session
- Session 6
- Focus
- Complete a mixed calendar set
- Proof you are ready
- Score at least 90% and justify every period, leap status, closing day, daily rate, entry, rounding choice, and qualifier.
Do not count recognition as mastery. Close the notes and explain the rule, apply it to a new fact pattern, and identify why each distractor fails.
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Questions students ask about Calendar-Day Proration: Actual-Day Examples
What is calendar-day proration in real estate?
Calendar-day proration allocates a full-period amount using the actual number of calendar days in the applicable year or billing period. For an annual nonleap-year item, divide by 365, count the responsible actual days, and multiply. Use 366 only when a leap-year actual-day convention applies.
How do you count seller days in a calendar-year proration?
Write the seller's start and end dates, decide who gets closing day, and add actual days month by month. If seller owns through April 10 in a nonleap year, count 31 in January, 28 in February, 31 in March, and 10 in April, for 100 days.
How does closing-day ownership change the count?
It changes the responsible period by one day. If seller owns through April 10, seller has 100 days from January 1 in a nonleap year. If buyer owns on April 10, seller ends April 9 and has 99 days. State the allocation before counting.
What are the cumulative calendar-day numbers for each month?
At the end of each nonleap month, cumulative days are 31, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334, and 365. In a leap year, add one to every total from February onward.
How do you count buyer days after closing?
If the buyer owns on closing day and the period runs through December 31, buyer days equal total year days minus seller days. If seller owns through closing, buyer begins the next day. Use subtraction only when the two shares cover the same complete period without gaps or overlap.
How do you prorate a monthly rent using actual days?
Divide the month's amount by the actual number of days in that month when the stated method requires actual monthly days, then multiply by the responsible days. Do not divide a February monthly rent by 365 or use a 30-day assumption unless instructed.
How do leap years affect actual-day prorations?
A leap year contains February 29 and 366 calendar days. For a full-year actual-day calculation, the daily denominator may be 366 when directed. For a monthly February calculation, use 29 days. Confirm both the year and the stated convention.
How do you assign a tax proration debit and credit?
If the seller's accrued unpaid tax share will be paid later by the buyer, debit seller and credit buyer. If the seller prepaid an item that benefits the buyer after closing, the problem may call for a seller credit and buyer debit. Determine status before direction.
What is the best way to check an actual-day count?
Count the period a second way. Use cumulative day numbers, month-by-month addition, or full-year days minus the other party's days. The parties' counts should cover the intended period exactly once under the same closing-day allocation. For a full nonleap tax year, seller days plus buyer days should equal 365. If the total is 364 or 366, inspect closing day first. A leap-year full-period check should total 366.
Are these official Illinois broker exam questions?
No. They are original calculations aligned to the PSI Illinois broker outline effective June 24, 2026. Current Illinois property-tax guidance, current federal Closing Disclosure requirements, and current Illinois security-deposit law were checked through August 1, 2026.
Primary sources
- PSI Illinois Candidate Information Booklet dated June 24, 2026
- Illinois Department of Revenue, current seller property-tax responsibility at closing
- Illinois Department of Revenue, FY 2026 Property Tax Study
- 12 CFR 1026.38, current Closing Disclosure transaction-summary requirements
- Consumer Financial Protection Bureau, current guide to federal mortgage disclosure forms
- 765 ILCS 710, current Illinois Security Deposit Return Act
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.