- Official section
- National XI.B: Tax and Other Prorations
- Broker weight
- A named calculation within 7% of the national portion
- Expected scored items
- The current PSI broker outline assigns about 7 of 100 scored national items to Real Estate Math
Real estate proration math guide
Choose the day-count convention before counting days
The annual amount is only half the setup. The other half is the clock. A 360-day problem uses a 12-by-30 classroom year; a 365-day problem uses actual calendar days in a nonleap year. Write the method and the party responsible for closing day before finding a daily rate.
Last updated: August 1, 2026
What calculation do you need to make?
Short answer: Under a 360-day method, daily rate equals annual amount divided by 360 and each full month is treated as 30 days under the stated convention. Under a 365-day method, daily rate equals annual amount divided by 365 and the responsible period uses actual calendar days. A leap-year actual-day problem can require 366 when expressly directed. Before calculating, determine whether the item is accrued or prepaid, which party owns or benefits from each period, who gets closing day, and whether the question wants one party's share or the settlement entry. Prorated amount equals daily rate times responsible days. Accrued unpaid seller-period taxes commonly create a seller debit and buyer credit because the buyer will later pay the bill. A prepaid seller item can produce the opposite reimbursement. Keep daily-rate precision until final cents and never blend day counts from one method with the denominator from another.
Day-count and closing-day conventions come from the question, contract, applicable law, loan or lease documents, settlement instructions, and local practice. The 360-day and 365-day methods here are exam frameworks, not universal commands for every Illinois closing. Actual property-tax prorations can use agreed tax factors, prior bills, anticipated changes, exemptions, installment timing, and later reproration provisions. Federal Closing Disclosure rules govern presentation for covered transactions but do not create one universal substantive allocation between buyer and seller. This is exam preparation, not legal, tax, lending, or closing advice. Sources were checked through August 1, 2026.
How do you choose between 360-day and 365-day proration?
- Write the full-period amount, item type, due status, requested party, and requested settlement entry before any division or date counting begins.
- Circle the stated 360-day, 365-day, 366-day, or actual-calendar convention before counting dates on exam day.
- Determine whether seller or buyer is responsible for closing day and write the exact start and end dates.
- Divide the annual amount by the matching denominator while preserving daily-rate precision.
- Count responsible days using 30-day months for the 360 method or actual month lengths for the actual-day method.
- Multiply daily rate by responsible days and round the final money amount as instructed.
- Decide debit and credit from accrued or prepaid status and which party pays or benefits outside its period.
- Reverse-check the two periods, reject any mixed-method hybrid, and label the convention in the final answer.
- Feature
- Year denominator
- 360-day method
- 360
- 365 or actual-day method
- 365, or 366 if directed
- Feature
- Month assumption
- 360-day method
- 30 days
- 365 or actual-day method
- Actual month length
- Feature
- Daily rate
- 360-day method
- Annual / 360
- 365 or actual-day method
- Annual / 365 or 366
- Feature
- Full month
- 360-day method
- 30 days
- 365 or actual-day method
- 28, 29, 30, or 31
- Feature
- Closing day
- 360-day method
- Use stated allocation
- 365 or actual-day method
- Use stated allocation
- Feature
- Seller days
- 360-day method
- 30-day convention
- 365 or actual-day method
- Actual calendar count
- Feature
- Buyer days
- 360-day method
- 360 - seller days when valid
- 365 or actual-day method
- Year days - seller days when valid
- Feature
- Prorated amount
- 360-day method
- Daily rate x days
- 365 or actual-day method
- Daily rate x days
- Feature
- Rounding
- 360-day method
- Final cents unless directed
- 365 or actual-day method
- Final cents unless directed
- Feature
- Main warning
- 360-day method
- Do not use actual month lengths
- 365 or actual-day method
- Do not assume every month has 30 days
Can you follow the calculation from facts to answer?
Use a 360-day proration
Scenario: Annual property tax is $7,200. A stated 360-day problem assigns 125 days to the seller. What is the seller share?
- $7,200 / 360 = $20 per day.
- $20 x 125 = $2,500.
- The problem supplies the day count, so no calendar recount is needed.
Answer: The seller's 360-day share is $2,500.
Use a 365-day proration
Scenario: Annual property tax is $7,300. A stated 365-day problem assigns 125 actual days to the seller. What is the seller share?
- $7,300 / 365 = $20 per day.
- $20 x 125 = $2,500.
- The matching denominator and actual-day count are explicit.
Answer: The seller's 365-day share is $2,500.
Compare methods with the same annual amount and days
Scenario: Annual rent is $18,000 and a classroom comparison uses 75 responsible days under each denominator. What are the two shares?
- 360-day share is $18,000 / 360 x 75 = $3,750.
- 365-day share is $18,000 / 365 x 75 = $3,698.63 after final rounding.
- The 360-day daily rate is larger because its denominator is smaller.
Answer: The shares are $3,750 under 360 days and $3,698.63 under 365 days.
Assign closing day before counting
Scenario: A nonleap-year actual-day problem closes April 10 and says the buyer owns on closing day. How many seller days run from January 1?
- Seller responsibility ends April 9.
- January 31 + February 28 + March 31 + April 9 = 99 days.
- If the seller owned through closing instead, the count would be 100.
Answer: The seller has 99 actual days under the stated allocation.
Handle an accrued tax entry
Scenario: A stated seller-period tax share is $3,240 and the buyer will later pay the unpaid bill. What simplified entry applies?
- The tax is accrued and unpaid for the seller's period.
- The buyer needs a credit because the buyer will later pay that share.
- The balanced opposite entry is a seller debit.
Answer: Debit seller and credit buyer $3,240.
Avoid premature daily-rate rounding
Scenario: Annual tax is $8,765 under a 365-day method, and the responsible period is 200 days. What is the share?
- $8,765 / 365 = $24.01369863 per day before rounding.
- $24.01369863 x 200 = $4,802.739726.
- Round the final amount to $4,802.74. Rounding the daily rate to $24.01 first would produce $4,802.00.
Answer: The 365-day prorated share is $4,802.74.
Which math errors cost the most points?
- Trap
- Use 360 because the question involves real estate.
- Correction
- Use the day-count convention expressly stated by the problem or transaction.
- Trap
- Divide by 365 but count 30-day months.
- Correction
- Match an actual-day denominator with actual calendar days.
- Trap
- Divide by 360 but count every 31st day.
- Correction
- Follow the stated 30-day-month convention consistently.
- Trap
- Use 365 automatically in a leap year.
- Correction
- Check whether the actual-day instructions require a 366-day denominator.
- Trap
- Count closing day for both parties.
- Correction
- Assign it once under the stated ownership convention.
- Trap
- Count closing day for neither party.
- Correction
- Ensure the two periods cover the intended year without a gap.
- Trap
- Choose debit and credit before identifying accrued or prepaid status.
- Correction
- Determine who paid, who benefited, and who will pay later first.
- Trap
- Treat an accrued seller tax as a seller credit.
- Correction
- If buyer will pay the seller-period bill later, debit seller and credit buyer.
- Trap
- Round the daily rate to cents immediately.
- Correction
- Carry precision and round the final prorated money unless instructed otherwise.
- Trap
- Assume both methods should produce the same amount.
- Correction
- Different denominators and day counts can create different contract allocations.
- Trap
- Use full-year minus seller days when periods do not cover the same full year.
- Correction
- Count the requested responsibility period directly when there are gaps or a different term.
- Trap
- Call a proration estimate the final property-tax liability.
- Correction
- A settlement allocation does not replace the taxing authority's bill and current contract terms.
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. Annual tax is $9,000. What is the daily rate under a 360-day method?
- $25
- $24.66
- $750
- $30
Show answer and explanation
Answer: $25
$9,000 / 360 = $25 per day.
2. Annual tax is $7,300. What is the daily rate under a 365-day method?
- $20
- $20.28
- $608.33
- $24
Show answer and explanation
Answer: $20
$7,300 / 365 = $20 per day.
3. A nonleap-year actual-day closing is April 10, and buyer owns on closing day. How many seller days run from January 1?
- 99 days
- 100 days
- 90 days
- 101 days
Show answer and explanation
Answer: 99 days
Count January 31, February 28, March 31, and April 1 through 9.
4. Who receives the credit for an accrued unpaid seller-period property tax that the buyer will pay later?
- Buyer
- Seller
- Listing broker
- Tax assessor
Show answer and explanation
Answer: Buyer
The buyer receives a credit and the seller receives the matching debit.
5. Which setup is internally consistent?
- Annual amount divided by 365 times actual calendar days
- Annual amount divided by 365 times 30-day months
- Annual amount divided by 360 times actual 31-day months
- Annual amount divided by 12 times 365
Show answer and explanation
Answer: Annual amount divided by 365 times actual calendar days
The denominator and day-count convention match.
Which numbers and formulas are easy to confuse?
- Terms
- 360-day vs. 365-day method
- Difference
- The 360-day method uses 12 assumed 30-day months. The 365-day method uses actual nonleap calendar days.
- Question cue
- Commercial classroom year versus actual calendar year.
- Terms
- 365-day vs. 366-day year
- Difference
- A 365 denominator fits a nonleap actual year. A 366 denominator can fit an expressly stated leap-year actual-day method.
- Question cue
- Ordinary year versus leap year.
- Terms
- Daily rate vs. day count
- Difference
- Daily rate comes from annual amount divided by the method denominator. Day count measures the responsible period.
- Question cue
- Dollars per day versus number of days.
- Terms
- Seller owns through closing vs. buyer owns on closing
- Difference
- The first includes closing day in seller time. The second assigns it to buyer time.
- Question cue
- Inclusive seller day versus exclusive seller day.
- Terms
- Accrued vs. prepaid
- Difference
- Accrued means incurred but not yet paid. Prepaid means paid before the benefit period is complete.
- Question cue
- Owed later versus paid already.
- Terms
- Prorated share vs. settlement entry
- Difference
- The share is the allocated amount. The entry identifies who is debited and credited.
- Question cue
- How much versus who pays whom.
- Terms
- Actual tax bill vs. estimated proration
- Difference
- The bill is issued under the taxing process. A closing proration can use an estimate or agreed factor before the bill is known.
- Question cue
- Government charge versus contract allocation.
- Terms
- Calendar count vs. date subtraction
- Difference
- A calendar count follows inclusive or exclusive responsibility. Raw date subtraction can omit the first or last day depending on convention.
- Question cue
- Ownership days versus elapsed intervals.
- Terms
- Final rounding vs. daily-rate rounding
- Difference
- Final rounding preserves intermediate precision. Daily-rate rounding can multiply a small error across many days.
- Question cue
- Round once versus compound rounding error.
- Terms
- Exam method vs. contract method
- Difference
- The exam uses the convention stated in the stem. A transaction uses current contract and settlement instructions.
- Question cue
- Question rule versus closing rule.
What does the outline expect you to calculate?
- Topic
- Proration purpose
- What to know
- Allocation, ownership period, benefit period, payment timing, closing, fair share, annual amount, prepaid item, accrued item, and settlement adjustment
- Best exam move
- Identify whose period is being allocated before doing day-count arithmetic.
- Topic
- Annual amount
- What to know
- Property tax, rent, insurance, association charge, interest, service contract, annual bill, known amount, estimated amount, and tax factor
- Best exam move
- Use the full-period amount supplied and label whether it is actual or estimated.
- Topic
- 360-day year
- What to know
- Twelve months, 30-day month, 360 denominator, banker year, classroom method, daily rate, monthly shortcut, and instruction
- Best exam move
- Divide annual amount by 360 and use the matching 30-day-month count.
- Topic
- 365-day year
- What to know
- Actual calendar, nonleap year, 365 denominator, month lengths, daily rate, actual days, January through December, and instruction
- Best exam move
- Divide by 365 and count the actual responsible calendar days.
- Topic
- 366-day leap year
- What to know
- February 29, leap year, actual-year denominator, stated convention, calendar days, daily rate, and date check
- Best exam move
- Use 366 only when the actual-day convention or problem expressly requires it.
- Topic
- Daily rate
- What to know
- Annual amount, denominator, division, dollars per day, precision, rounding, recurring charge, and method label
- Best exam move
- Carry enough decimal precision until the final proration amount.
- Topic
- 360-day count
- What to know
- Full 30-day month, partial month, day number, 31st, February, start date, end date, inclusive count, and convention
- Best exam move
- Follow the exact 30-day rule supplied rather than mixing actual month lengths.
- Topic
- Actual-day count
- What to know
- January 31, February 28 or 29, April 30, month table, cumulative days, inclusive day, exclusive day, and date range
- Best exam move
- Write each month's responsible days and add them before multiplying.
- Topic
- Closing-day allocation
- What to know
- Seller owns through closing, buyer owns on closing, day before closing, include, exclude, possession, contract convention, and responsibility
- Best exam move
- State which party receives closing day before counting either share.
- Topic
- Seller-day method
- What to know
- January 1, closing date, seller period, days elapsed, through closing, before closing, accrued amount, and subtraction check
- Best exam move
- Count only the seller's responsible period when finding the seller adjustment.
- Topic
- Buyer-day method
- What to know
- Day after seller period, year end, remaining days, buyer period, prepaid item, reimbursement, full year minus seller days, and check
- Best exam move
- Use total convention days minus seller days only when the periods cover the same full year without gaps or overlap.
- Topic
- Accrued item
- What to know
- Used but unpaid, property tax in arrears, rent earned, interest accrued, seller responsibility, buyer later pays, debit, and credit
- Best exam move
- Charge the party who incurred the unpaid share and credit the party who will bear the later payment.
- Topic
- Prepaid item
- What to know
- Paid in advance, insurance, rent, association fee, seller payment, buyer benefit, reimbursement, seller credit, and buyer debit
- Best exam move
- Reimburse the party who paid for the other party's post-closing benefit when the problem directs.
- Topic
- Debit and credit
- What to know
- Seller debit, seller credit, buyer debit, buyer credit, balanced entry, ledger, cash to close, seller net, and direction
- Best exam move
- Name both sides after calculating the amount rather than deciding direction from a memorized sign alone.
- Topic
- Method comparison
- What to know
- Same annual amount, 360 daily rate, 365 daily rate, different day counts, dollar difference, convention, estimate, and no hybrid
- Best exam move
- Calculate each method independently before comparing results.
- Topic
- Rounding
- What to know
- Daily rate, cents, intermediate digits, final amount, whole dollar, instruction, cumulative difference, and calculator memory
- Best exam move
- Round final money to cents unless the problem directs another rule.
- Topic
- Reverse check
- What to know
- Seller days plus buyer days, 360, 365, 366, full-period amount, two shares, daily rate, and reconciliation
- Best exam move
- Confirm the two responsibility periods cover the intended full period once, without a missing or double-counted day.
- Topic
- Illinois property-tax context
- What to know
- Tax year, paid in arrears, seller responsibility, closing, prior bill, estimate, factor, exemption change, reproration, and agreement
- Best exam move
- Use the stated tax amount and allocation without assuming a classroom result is a final Illinois tax bill.
How should you drill this calculation?
- Session
- Session 1
- Focus
- Choose the convention
- Proof you are ready
- Classify 30 stems as 360-day, 365-day, 366-day, actual-calendar, or insufficiently specified.
- Session
- Session 2
- Focus
- Calculate daily rates
- Proof you are ready
- Calculate and compare 25 annual amounts under 360 and 365 denominators without premature rounding.
- Session
- Session 3
- Focus
- Count responsibility days
- Proof you are ready
- Count 20 seller and buyer periods under stated closing-day allocations for both methods.
- Session
- Session 4
- Focus
- Post debits and credits
- Proof you are ready
- Classify 30 accrued and prepaid tax, rent, insurance, and association items by amount, debit, and credit.
- Session
- Session 5
- Focus
- Compare and reverse-check
- Proof you are ready
- Solve 20 paired-method comparisons and reconcile the two party periods to the full convention year.
- Session
- Session 6
- Focus
- Complete a mixed proration set
- Proof you are ready
- Score at least 90% and justify every denominator, date count, closing day, status, entry, precision 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 360-Day vs. 365-Day Real Estate Proration
What is the 360-day proration method?
A simplified 360-day method treats the year as 12 months of 30 days. The daily rate is the annual amount divided by 360. For a partial date span, count the responsible 30-day-month days under the convention stated in the question, then multiply by the daily rate. This is not automatically the same as prorating by whole months. A daily 360 calculation can include a partial 30-day month, while a monthly calculation may allocate only complete monthly periods under different instructions.
What is the 365-day proration method?
The 365-day method divides the annual amount by 365 and multiplies by the actual responsible calendar days stated or counted. In a leap year, use 366 only when the problem or governing convention calls for actual days in that leap year.
Which proration method should I use on the Illinois broker exam?
Use the method expressly supplied by the problem. The PSI outline tests prorations but does not make one classroom day-count convention universally controlling. Look for 360-day year, 365-day year, actual days, 30-day months, calendar method, or a direct instruction.
Why do 360-day and 365-day answers differ?
They use different daily rates and can use different day counts. Dividing the same annual amount by 360 produces a slightly larger daily rate than dividing by 365. A 30-day-month count can also differ from actual calendar days in February and 31-day months.
Who gets the closing day in a proration?
The party identified by the problem, contract, local practice, or settlement instruction. If the seller owns through closing, include closing day in the seller period. If the buyer owns on closing day, end the seller period the day before. Never assume without reading the stated convention.
How do you count days under a 360-day method?
Use the problem's 30-day-month convention. One common classroom count assigns 30 days to each full month and then adds the stated partial-month days. Dates on the 31st and end-of-February handling can follow specialized conventions, so use the exact instruction rather than inventing one.
How do you count days under a 365-day method?
Count actual calendar days in the responsible period, following the closing-day allocation. A quick cumulative-day table or month-by-month list reduces errors. Verify February and leap-year status before finalizing the count.
What is the debit and credit for accrued property tax?
When the seller owes the buyer for an accrued unpaid tax period that the buyer will later pay, the simplified entry is a seller debit and buyer credit. The direction follows who benefited from the period and who will pay the later bill, not merely which party brings cash to closing.
Should I round the daily proration rate?
Unless instructed otherwise, keep enough precision in the daily rate and round the final money result to cents. Rounding the daily rate too early can change the final amount across many days. Show the convention, count, and final rounding.
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 Department of Revenue property-tax guidance and current federal Closing Disclosure requirements 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
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.