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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.

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

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?

  1. Identify the full-period amount, billing period, due status, requested party, and requested settlement entry.
  2. Confirm the year, leap status, actual-day convention, and which party owns or benefits on closing day.
  3. Write the responsible start and end dates and count actual days month by month or through cumulative day numbers.
  4. Divide an annual amount by 365 or 366, or divide a monthly amount by that month's actual number of days.
  5. Multiply the unrounded daily rate by the responsible days and round only the final amount as instructed.
  6. Identify accrued, prepaid, collected, or held status before deciding seller and buyer debit-credit direction.
  7. Count the other party's period independently or use a valid full-period complement to confirm no missing or duplicated calendar day remains.
  8. 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?

  1. Month-end cumulative days through April equal 120.
  2. Include May 1 through 15: 120 + 15 = 135.
  3. 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?

  1. The seller's final day is May 14.
  2. Cumulative days through April are 120, plus 14 May days.
  3. 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.

  1. $9,125 / 365 = $25 per day.
  2. $25 x 135 = $3,375.
  3. 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?

  1. $7,320 / 366 = $20 per day.
  2. $20 x 91 = $1,820.
  3. 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?

  1. Leap-year February has 29 days.
  2. $2,900 / 29 = $100 per day.
  3. $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?

  1. $6,500 / 365 = $17.80821918 per day before rounding.
  2. $17.80821918 x 200 = $3,561.643836.
  3. 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?

  1. 90 days
  2. 89 days
  3. 91 days
  4. 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?

  1. 100 days
  2. 99 days
  3. 101 days
  4. 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?

  1. $20
  2. $20.05
  3. $610
  4. $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?

  1. $100
  2. $103.33
  3. $8.49
  4. $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?

  1. Debit seller and credit buyer
  2. Credit seller and debit buyer
  3. Debit both parties
  4. 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

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.

Read our editorial and corrections process

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