Skip to content

Closing math guide

Real estate proration from time share to ledger entry

Proration has three separate jobs: choose the money base, count the time, and decide who owes whom. Do them in that order. Students who chase debit and credit labels before they know who paid usually reverse a perfectly correct dollar calculation.

Last updated: August 1, 2026

What calculation do you need to make?

Short answer: Prorated share equals the full-period amount divided by the stated time units, multiplied by the responsible units. For an accrued seller-period expense the buyer will pay later, use a seller debit and buyer credit. For a seller-prepaid expense benefiting the buyer, use a seller credit and buyer debit. Rent the seller collected in advance for the buyer period normally creates a seller debit and buyer credit. Count closing day for the party named in the question. Use 30-day months only in a stated 360-day method; use actual days for a calendar method. Build an estimated annual base before calculating when the contract requires a percentage of the prior bill.

Official section
National XI.C: Prorations for Tax and Other Items
Broker weight
A named skill 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

The current PSI outline expressly names prorations for tax and other items. Actual Illinois settlement entries follow the contract, tax-bill status, local practice, lender instructions, title records, lease terms, applicable landlord law, and any reproration agreement. A prior bill can be an estimate rather than the final liability. The federal Closing Disclosure shows charges and adjustments but does not replace the parties' contract. Use the amount, method, period, closing-day owner, and payment status stated in the exam question. Sources were checked through August 1, 2026.

How do you solve real estate prorations?

  1. Box the item, full-period amount, period covered, proration method, closing date, and owner of closing day.
  2. Classify the item as accrued expense, prepaid expense, accrued income, prepaid income, or transferred liability.
  3. Build any adjusted annual base, such as 105% of the prior tax bill, before finding a unit rate.
  4. Divide the full-period amount by the stated months, 360 days, 365 days, 366 days, or actual period units.
  5. Count the responsible units visibly and multiply them by the unrounded unit rate.
  6. Ask who paid or collected, who benefited or earned, and who will pay or collect after closing.
  7. Enter matching buyer and seller debits or credits without counting the same item twice.
  8. Reconcile the party shares to the full amount and round only as the question directs.
Situation
Unpaid seller-period expense
Normal entry
Seller debit, buyer credit
Reason
Buyer will pay seller share
Situation
Seller prepaid buyer-period expense
Normal entry
Seller credit, buyer debit
Reason
Buyer reimburses seller
Situation
Seller-period income buyer will collect
Normal entry
Seller credit, buyer debit
Reason
Buyer passes earned income back
Situation
Seller collected buyer-period income
Normal entry
Seller debit, buyer credit
Reason
Seller passes unearned income forward
Situation
Daily rate
Normal entry
Full-period amount / stated days
Reason
Use one convention
Situation
Prorated share
Normal entry
Unit rate x responsible units
Reason
Count closing day correctly
Situation
Estimated annual base
Normal entry
Prior amount x stated factor
Reason
Adjust before daily rate
Situation
Buyer owns closing day
Normal entry
Seller ends day before
Reason
Exclude closing date from seller
Situation
Seller owns closing day
Normal entry
Seller includes closing date
Reason
One extra seller day
Situation
Transferred security deposit
Normal entry
Seller debit, buyer credit
Reason
Liability moves to buyer

Can you follow the calculation from facts to answer?

Prorate unpaid taxes with a 365-day year

Scenario: Annual property taxes are $8,760. The problem uses 365 days and charges the seller with 150 days. The buyer will pay the bill later.

  1. $8,760 / 365 = $24 per day.
  2. $24 x 150 seller days = $3,600.
  3. Because the buyer will later pay the seller-period expense, debit seller and credit buyer.

Answer: The $3,600 proration is a seller debit and buyer credit.

Use a 360-day tax method

Scenario: A stated annual expense is $7,200. Under a 360-day method, the seller is charged for four 30-day months and 12 additional days.

  1. Daily rate is $7,200 / 360 = $20.
  2. Seller time is (4 x 30) + 12 = 132 days.
  3. $20 x 132 = $2,640.

Answer: The seller's share is $2,640 before assigning direction from payment status.

Reimburse a prepaid association expense

Scenario: The seller paid $1,200 of association dues for the calendar year. Closing is October 1, the buyer owns closing day, and the problem prorates by whole months.

  1. Monthly dues are $1,200 / 12 = $100.
  2. The buyer owns October, November, and December, or three months, worth $300.
  3. The seller already paid for those buyer months, so the buyer reimburses the seller.

Answer: Enter a $300 seller credit and $300 buyer debit.

Transfer rent received in advance

Scenario: The seller collected $3,000 rent for a 30-day month. Closing occurs after 12 seller days, and the buyer owns the remaining 18 days.

  1. Daily rent is $3,000 / 30 = $100.
  2. Buyer-period rent is $100 x 18 = $1,800.
  3. The seller holds rent earned during buyer ownership and owes it to the buyer.

Answer: Enter a $1,800 seller debit and $1,800 buyer credit.

Adjust the prior tax bill before prorating

Scenario: The contract requires proration at 105% of the prior $7,200 bill. It uses a 360-day year and 100 seller days.

  1. Estimated annual base is $7,200 x 1.05 = $7,560.
  2. Daily rate is $7,560 / 360 = $21.
  3. Seller share is $21 x 100 = $2,100.

Answer: The estimated seller tax share is $2,100.

Separate deposit transfer from rent

Scenario: At closing the seller holds a $2,500 refundable tenant security deposit and has also collected $1,800 of rent attributable to the buyer's ownership period.

  1. The $2,500 deposit is a tenant-related liability, not earned rent.
  2. The $1,800 is buyer-period income already collected by the seller.
  3. Both amounts move economically to the buyer, but they retain different legal and accounting labels.

Answer: Credit buyer and debit seller $4,300 total, recorded as separate $2,500 deposit and $1,800 rent entries.

Which math errors cost the most points?

Trap
Every proration is a seller debit and buyer credit.
Correction
Prepaid seller expenses benefiting the buyer reverse that direction.
Trap
Assign debits and credits before identifying payment status.
Correction
First decide who paid or collected and which party owns the relevant period.
Trap
Use 360 days for every closing problem.
Correction
Use the stated 360-day, 365-day, leap-year, monthly, or calendar method.
Trap
Treat actual February as 28 days in a 360-day method.
Correction
A stated 360-day method treats every month as 30 days.
Trap
Include closing day for both buyer and seller.
Correction
Assign it to the party specified so the day is counted once.
Trap
Apply 105% after calculating the seller's share.
Correction
Build the adjusted annual base first, then calculate its unit and party shares.
Trap
Round a repeating daily rate before multiplying.
Correction
Retain full precision and round the final proration unless instructed otherwise.
Trap
Treat rent collected in advance as entirely the seller's income.
Correction
Transfer the portion attributable to buyer ownership through a buyer credit.
Trap
Treat a refundable security deposit as rent.
Correction
The deposit is a tenant-related liability and should be transferred separately.
Trap
Call an estimated tax proration the final tax bill.
Correction
An estimate can be subject to the contract and a later reproration.
Trap
Use the bill due date as the ownership period automatically.
Correction
Identify the tax or service period the bill covers, which can differ from its payment date.
Trap
Count the same proration as a fee and an adjustment.
Correction
Record each economic item once on each party's ledger.

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. An annual expense is $7,300. Using 365 days and 90 responsible days, what is the prorated share?

  1. $1,800
  2. $2,000
  3. $1,825
  4. $657
Show answer and explanation

Answer: $1,800

$7,300 / 365 = $20 per day, and $20 x 90 = $1,800.

2. The seller prepaid an expense that benefits the buyer after closing. What is the normal direction?

  1. Seller credit and buyer debit
  2. Seller debit and buyer credit
  3. Debit both parties
  4. Credit both parties
Show answer and explanation

Answer: Seller credit and buyer debit

The buyer reimburses the seller for the buyer-period benefit already paid by the seller.

3. A prior $8,000 tax bill is prorated at 105%. What annual base should be used before counting days?

  1. $8,400
  2. $8,000
  3. $8,105
  4. $7,619.05
Show answer and explanation

Answer: $8,400

$8,000 x 1.05 = $8,400.

4. The seller collected rent for a period the buyer will own. What is the normal direction for the buyer-period amount?

  1. Seller debit and buyer credit
  2. Seller credit and buyer debit
  3. No adjustment
  4. Buyer debit only
Show answer and explanation

Answer: Seller debit and buyer credit

The seller passes the buyer-period income already collected to the buyer.

5. Under a 360-day method, how many days are in four full months plus 15 days?

  1. 135 days
  2. 137 days
  3. 120 days
  4. 145 days
Show answer and explanation

Answer: 135 days

Four 30-day months equal 120 days; add 15 to get 135.

Which numbers and formulas are easy to confuse?

Terms
Accrued expense vs. prepaid expense
Difference
An accrued expense was incurred but remains unpaid. A prepaid expense was paid before the benefiting period ended.
Question cue
Future payment versus prior payment.
Terms
Accrued income vs. prepaid income
Difference
Accrued income was earned but not collected. Prepaid income was collected before the full earning period.
Question cue
Earned first versus collected first.
Terms
Dollar share vs. ledger direction
Difference
The dollar share measures time allocation. Ledger direction decides which party reimburses the other.
Question cue
How much versus who owes whom.
Terms
360-day vs. 365-day method
Difference
A 360-day method uses twelve 30-day months. A 365-day method uses a 365 denominator and the required actual-day count.
Question cue
Synthetic year versus ordinary calendar denominator.
Terms
365-day vs. leap-year method
Difference
An ordinary calendar year has 365 days. A leap year has 366 and includes February 29.
Question cue
Ordinary year versus leap year.
Terms
Tax bill vs. proration base
Difference
The last tax bill is an official historical amount. The contract may adjust it by a stated percentage to create an estimated base.
Question cue
Known bill versus agreed estimate.
Terms
Proration vs. reproration
Difference
Proration makes the closing allocation. Reproration revisits an estimate after the actual amount becomes known.
Question cue
Closing estimate versus later true-up.
Terms
Rent proration vs. security-deposit transfer
Difference
Rent is income allocated to an earning period. A refundable deposit remains a tenant-related liability until lawfully applied or returned.
Question cue
Earned income versus held funds.
Terms
Buyer credit vs. buyer debit
Difference
A buyer credit reduces buyer cash needed. A buyer debit increases the buyer's settlement obligation.
Question cue
Money toward buyer versus money due from buyer.
Terms
Paid item vs. responsible party
Difference
The party who wrote the check is not always the party economically responsible for the entire period.
Question cue
Payment timing versus ownership share.

What does the outline expect you to calculate?

Topic
Purpose of proration
What to know
Ownership period, benefit period, income, expense, allocation, reimbursement, accrued item, prepaid item, collected income, unpaid income, settlement adjustment, and fair share
Best exam move
Identify which party owned or benefited during the period before calculating the adjustment.
Topic
Full-period amount
What to know
Annual tax, annual premium, monthly rent, annual association fee, quarterly charge, fuel amount, water bill, assessment, estimated amount, prior bill, contract factor, and proration base
Best exam move
Build the exact full-period base required before dividing it into time units.
Topic
Accrued expenses
What to know
Unpaid property tax, utility used, association charge incurred, interest owed, seller ownership, buyer future payment, seller debit, buyer credit, reimbursement, and liability
Best exam move
When the buyer will pay the seller's incurred share later, transfer that amount from seller to buyer at closing.
Topic
Prepaid expenses
What to know
Prepaid insurance, prepaid association dues, prepaid tax, fuel supply, service contract, seller prior payment, buyer future benefit, seller credit, buyer debit, and reimbursement
Best exam move
Give the seller credit for the buyer-period benefit the seller already funded.
Topic
Accrued income
What to know
Rent earned but uncollected, tenant arrears, seller ownership period, buyer later collection, seller credit, buyer debit, collectability, lease, and transaction instruction
Best exam move
If the buyer will collect income earned during seller ownership and the problem treats it as collectible, reimburse the seller.
Topic
Prepaid income
What to know
Rent received in advance, tenant payment, buyer ownership period, seller collection, unearned portion, seller debit, buyer credit, monthly rent, daily rent, and lease period
Best exam move
Transfer the buyer-period income already held by the seller to the buyer.
Topic
Property-tax estimate
What to know
Prior bill, current estimate, 100%, 105%, 110%, contract factor, new construction, reassessment, exemption, seller occupancy, annual base, and reproration
Best exam move
Multiply the prior bill by the stated factor before finding any daily rate.
Topic
Illinois property-tax direction
What to know
Outstanding bill, seller responsibility, buyer future payment, seller period, buyer credit, seller debit, closing date, contract terms, county treasurer, and reproration
Best exam move
For an unpaid seller-period share the buyer will pay, debit the seller and credit the buyer.
Topic
Monthly proration
What to know
Full month, partial month, monthly rent, monthly dues, daily rent, month length, closing date, buyer days, seller days, and exact instruction
Best exam move
Use whole months only when allowed, then calculate any partial month under the stated convention.
Topic
360-day method
What to know
Banker's year, statutory year, twelve months, 30-day month, annual amount, daily rate, month number, synthetic day count, February, and instruction
Best exam move
Divide by 360 and treat each month as 30 days only when the problem expressly chooses this method.
Topic
365-day method
What to know
Annual amount, 365 denominator, daily rate, elapsed days, ownership days, ordinary year, closing day, inclusive count, and exact calculation
Best exam move
Divide by 365, count the required days, and retain precision until the final amount.
Topic
Leap-year method
What to know
366 days, February 29, leap year, annual amount, daily rate, calendar count, closing date, denominator, and problem instruction
Best exam move
Use 366 only when the relevant year and stated calendar convention require it.
Topic
Calendar-day counting
What to know
January 31, February 28 or 29, April 30, June 30, September 30, November 30, full months, partial month, closing day, and cumulative days
Best exam move
Write each month subtotal so the responsible period and any off-by-one choice remain visible.
Topic
Closing-day allocation
What to know
Buyer owns closing day, seller owns closing day, through day before closing, include closing date, possession, proration date, contract, and one-day difference
Best exam move
Write B or S on the closing date before counting either party's days.
Topic
Debit and credit direction
What to know
Buyer debit, buyer credit, seller debit, seller credit, cash needed, seller proceeds, matching entry, settlement ledger, reimbursement, and economic direction
Best exam move
Name who paid, who benefited, and who will pay before assigning accounting labels.
Topic
Security-deposit liability
What to know
Tenant deposit, refundable amount, accrued interest, lawful deduction, transfer, buyer-held liability, seller debit, buyer credit, notice, records, and rent distinction
Best exam move
Treat transferred deposit money as a liability, not rent earned during an ownership period.
Topic
Closing Disclosure
What to know
Summaries of transactions, adjustments for items paid by seller in advance, adjustments for items unpaid by seller, due from buyer, due to seller, borrower credit, seller credit, and final cash
Best exam move
Read the economic direction behind the line instead of assuming the word credit always helps the same party.
Topic
Precision and reconciliation
What to know
Daily rate, repeating decimal, full precision, cents, final rounding, total period, buyer share, seller share, sum check, sign, and answer choice
Best exam move
Confirm that both party shares add to the full-period amount and round only at the directed stage.

How should you drill this calculation?

Session
Session 1
Focus
Classify proration stories
Proof you are ready
Sort 40 facts into accrued expense, prepaid expense, accrued income, prepaid income, or transferred liability.
Session
Session 2
Focus
Count time accurately
Proof you are ready
Count 20 seller and buyer periods under explicit closing-day, monthly, calendar, and leap-year instructions.
Session
Session 3
Focus
Use every day method
Proof you are ready
Solve ten 360-day, ten 365-day, and ten calendar-day prorations with full-precision checks.
Session
Session 4
Focus
Assign ledger direction
Proof you are ready
Enter matching buyer and seller debits or credits for 25 paid, unpaid, collected, and uncollected items.
Session
Session 5
Focus
Handle estimates and rental items
Proof you are ready
Build adjusted tax bases, rent allocations, deposit transfers, and reproration explanations in 20 scenarios.
Session
Session 6
Focus
Complete a mixed proration set
Proof you are ready
Score at least 90% and justify each answer by item class, base, time method, day owner, responsible share, payment status, and direction.

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.

Build speed without skipping the setup

From concept to decision

Drill this topic, then review the explanation

Pass Illinois gives you original national and Illinois questions, topic-by-topic study, clear explanations, timed practice, flashcards, progress tracking, and Math Coach. Start free, find the weak distinction, and focus the next session there.

Questions students ask about Real Estate Proration Formula and Examples

What is the real estate proration formula?

Prorated share equals the full-period amount divided by the number of units in that period, multiplied by the responsible units. Units can be months or days. Use the 360-day, 365-day, 366-day, or actual-calendar method stated in the problem.

What is an accrued item at closing?

An accrued item has been earned or incurred but has not yet been paid or collected for the relevant period. When the buyer will later pay an expense attributable to the seller's ownership, the seller normally receives a debit and the buyer a matching credit, subject to the contract and problem facts.

What is a prepaid item at closing?

A prepaid item was paid before closing for a period extending beyond closing. If the seller paid an expense that benefits the buyer after closing, the buyer normally reimburses the seller through a buyer debit and seller credit for the buyer period.

Are Illinois property taxes prorated as accrued expenses?

Illinois closing questions commonly treat property tax as accrued because a bill for an ownership period is paid later. IDOR says an existing-home seller generally pays outstanding bills and provides a buyer credit for the seller's ownership period under the contract. Use the bill status and contract method stated in the problem.

Should a proration use 360 or 365 days?

Use the method stated. A 360-day method uses twelve 30-day months. A 365-day method divides the annual amount by 365 and then uses the required day count. A leap-year problem may use 366. Do not switch conventions halfway through the calculation.

Who owns the closing day in a proration problem?

The contract or question decides. If the buyer owns closing day, seller time ends the day before. If the seller owns closing day, include it in seller time. Write that assignment before counting to avoid an off-by-one error.

How is rent received in advance prorated?

If the seller already collected rent covering the buyer's post-closing ownership period, the seller owes that portion to the buyer. The adjustment is normally a seller debit and buyer credit. Calculate the buyer-period rent from the exact monthly or daily convention supplied.

Is a tenant security deposit rental income to prorate?

No. A refundable security deposit is generally a liability held for the tenant, not rent earned by the seller. At transfer, the applicable deposit and required records or notices follow governing law and the transaction. Keep a deposit transfer separate from a rent proration.

What is a tax reproration agreement?

It is an agreement to revisit an estimated closing allocation after the actual tax bill becomes available. IDOR notes that new-construction transactions often use a reproration agreement. The initial estimate and later true-up are separate calculations.

Are these official Illinois broker exam questions?

No. They are original calculations aligned to the PSI broker outline effective June 24, 2026. Current Illinois Department of Revenue materials, federal Closing Disclosure rules, and Illinois 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

Was this guide useful?

Choose one response. You can add a short note, especially if a rule, example, or explanation needs work. No name or email is requested.