Closing math guide
Count the days, then decide who owes whom
Getting the dollar amount right is only half the problem. A seller who prepaid the buyer's expense gets reimbursed. A seller holding rent for the buyer's ownership period owes that income to the buyer. Start with who paid, what period the money covers and who benefits.
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The short answer
Prorated share = full-period amount / stated period units x responsible units. Count closing day for the party named in the question. For an unpaid seller-period expense the buyer will pay, debit the seller and credit the buyer. For a seller-prepaid expense benefiting the buyer, credit the seller and debit the buyer. Rent already collected for the buyer's period normally creates a seller debit and buyer credit. Use the stated time convention and payment facts.
Reviewed October 25, 2026. National XI.A.3 in the June 24, 2026 PSI broker outline covers real property tax and other prorations. The entire Real Estate Calculations domain has 7 of 100 scored national questions, not seven proration questions. Every example below supplies its own assumptions. Illinois contracts, bill status, leases, applicable law and settlement instructions determine actual allocations; this page does not set a statewide closing-day or 105% tax-proration rule.
Solve the amount before entering the adjustment
- Identify the item and the period it covers. A bill due this year may relate to last year. Write down whether it is an expense, collected income, collectible but unpaid income, or a deposit liability. Do not use a due date as the beginning of the benefit period.
- Read the payment facts. Who has already paid or collected? Who will pay or collect after closing? If a seller pays an entire outstanding bill at closing, do not also credit the buyer for that same full bill as though the buyer will pay it later.
- Build the stated base. If the contract uses 105% of a $7,200 prior bill, the estimated annual base is $7,560. That percentage is a contract assumption, not proof of the next bill. The same unrounded result can be obtained by multiplying the calculated time share by 1.05.
- Write both parts of the time convention. For a stated 30/360 example, use 30-day months and a 360-day denominator. Actual-day counting is different. A 360-day denominator alone does not establish that every month has 30 days; Actual/ 360 exists in loan calculations. Do not import its lender-specific default into an Illinois tax problem. These examples avoid special month-end adjustments; follow any February or month-end rule supplied in a problem.
- Assign the proration date once. If the buyer receives closing day, the seller's share ends the day before. If the seller receives it, include it in seller time. The contract may use possession or another adjustment date, so do not substitute closing automatically.
- Calculate with full precision, then state who reimburses whom. Divide the full-period amount by the stated units and multiply by the responsible units. For a calendar allocation of a fixed period amount, the unrounded buyer and seller shares should add to that amount. Follow the requested cent rounding and reconcile any rounding penny rather than changing the day count.
| Given situation | Seller entry | Buyer entry |
|---|---|---|
| Buyer will pay an unpaid expense for seller time | Debit seller share | Credit same share |
| Seller already paid expense for buyer time | Credit buyer share | Debit same share |
| Seller collected income for buyer time | Debit buyer-period income | Credit same income |
| Buyer reimburses collectible seller-period income under stated terms | Credit agreed seller amount | Debit same amount |
| Seller-held refundable deposit credited to buyer at closing | Debit transferred liability amount | Credit same amount |
| Seller pays a full bill directly at closing | Record the payment as instructed | Do not also credit that full bill as unpaid to buyer |
The distinctions that matter
| Distinction | How it works | What to notice |
|---|---|---|
| Accrued expense vs. prepaid expense | An accrued expense has been incurred but remains unpaid. A prepaid expense has already been paid for a period extending beyond the adjustment date. | The same time share can produce opposite entries depending on who paid. |
| Prepaid income vs. prepaid expense | Rent the seller collected belongs partly to the buyer after transfer. Dues the seller paid may instead require the buyer to reimburse the seller. | Collected income and paid expense move in opposite directions. |
| 30/360 vs. Actual/ 360 | Both use 360 in the denominator, but only the named 30/360 convention uses synthetic 30-day months. Actual/ 360 uses actual calendar days. | Read the numerator convention as well as the denominator. |
| Actual/ 365 vs. actual-year allocation | Actual/ 365 uses 365 as specified. A calendar allocation of an entire leap-year annual amount can use 366 when that is the stated method. | Do not automatically change an express fixed denominator because a year is leap. |
| Proration estimate vs. tax payment | A buyer credit reallocates part of the expense between parties. It does not itself pay the county or guarantee the final tax amount. | Identify the covered tax year and whether the bill remains unpaid. |
| Deposit transfer vs. rent proration | A refundable deposit is a tenant-related liability, not rent earned day by day. A closing credit between owners does not erase tenant rights. | Keep separate labels, even when both entries point in the same direction. |
| Tax adjustment vs. lender escrow | A seller tax credit and the buyer's initial lender tax reserve serve different purposes. One does not automatically cancel or replace the other. | Check for separate settlement entries without double-counting the same payment. |
Work through the facts
Count actual days and assign closing day
The invented annual tax amount is $7,300. Use actual days over 365 in 2026. Closing is June 15, the buyer gets closing day, and the buyer will pay the full bill later.
- Seller days: January 31 + February 28 + March 31 + April 30 + May 31 + June 14 = 165.
- Daily amount: $7,300 / 365 = $20. Seller share: 165 x $20 = $3,300.
- Buyer has 200 days and a $4,000 share. The two shares total $7,300.
- If the seller instead gets closing day, seller days become 166 and seller share becomes $3,320.
Answer: With closing day assigned to the buyer, debit the seller and credit the buyer $3,300.
Apply an expressly stated 30/360 convention
An invented $7,200 annual expense uses 30-day months and a 360-day year. The buyer gets June 15; seller time runs January 1 through June 14. The buyer will pay the expense later.
- Five synthetic months plus 14 days = 5 x 30 + 14 = 164 seller days.
- $7,200 / 360 = $20 per day.
- Seller share:164 x $20 = $3,280. This is a stated 30/360 example, not an actual-day count.
Answer: Debit seller and credit buyer $3,280. Do not substitute the actual-calendar 165 days.
Reimburse prepaid association dues
The seller paid $1,200 dues for the calendar year. Closing is October 1, buyer gets closing day, and the problem expressly allocates by whole months.
- Monthly amount: $1,200 / 12 = $100.
- Buyer months: October, November and December = 3.
- Buyer share:3 x $100 = $300. The seller already paid it.
Answer: Credit the seller and debit the buyer $300.
Allocate collected rent in a 31-day month
The seller collected $3,100 July rent. The question uses actual days in July. The buyer gets July 11 and all remaining July days.
- Seller has July 1 through 10:10 days. Buyer has July 11 through 31:21 days.
- Daily rent: $3,100 / 31 = $100. Buyer-period rent:21 x $100 = $2,100.
- The seller holds $2,100 attributable to the buyer period.
Answer: Debit the seller and credit the buyer $2,100.
Build a tax estimate without inventing a tax rule
The contract specifies 105% of a prior $7,200 annual bill, a 360-day denominator and 100 seller days. Buyer will pay the estimated bill later.
- Estimated annual base: $7,200 x 1.05 = $7,560.
- Seller share: $7,560 / 360 x 100 = $2,100.
- Equivalent unrounded order: ($7,200 / 360 x 100) x 1.05 = $2,100.
Answer: Debit seller and credit buyer $2,100 under these assumptions. Neither 105% nor the resulting estimate is the final official tax bill.
Keep an older bill separate from current-year accrual
At a hypothetical April 11, 2026 closing, an unpaid 2025 tax bill is $8,000. The contract makes the seller responsible for all of it. It separately allocates the 2026 annual estimate of $7,300 using actual days over 365, gives closing day to buyer, and says buyer will pay both amounts later.
- Seller has 100 days of 2026: January 31 + February 28 + March 31 + April 10.
- Current-year share: $7,300 / 365 x 100 = $2,000.
- Separate prior-year bill: $8,000. Total seller debit and buyer credit: $8,000 + $2,000 = $10,000.
- If the seller instead pays the $8,000 bill directly at closing, do not also give buyer an $8,000 credit for paying it later.
Answer: The specified unpaid-bill arrangement produces $10,000 total, with the two tax years identified separately.
Use a leap-year denominator only when specified
A hypothetical 2028 problem allocates a $7,320 annual expense over the actual 366-day year. Buyer gets March 1. Buyer will pay the bill later.
- Seller time is January 31 + February 29 = 60 days.
- $7,320 / 366 = $20 per day.
- Seller share:60 x $20 = $1,200. Buyer share:306 x $20 = $6,120.
Answer: Debit seller and credit buyer $1,200 under the given actual-year method.
Separate a deposit from collected income
The question directs a closing credit for the seller's $2,500 refundable tenant deposit. Seller also holds $1,800 rent attributable entirely to the buyer period.
- Deposit transfer credit: $2,500, a tenant-related liability.
- Rent adjustment credit: $1,800, buyer-period income.
- Combined economic direction: $4,300 seller debit and buyer credit, shown as separate items.
Answer: Transfer the full stated deposit amount and the stated rent share separately. Do not prorate the deposit by days.
Mistakes to avoid
- Calling every 360-day denominator a 30-day-month method Read the named day-count convention. Actual/ 360 and 30/360 count months differently.
- Counting closing day twice Allocate the date once, to the named party.
- Giving a buyer credit for an expense the seller already prepaid For the buyer's benefit paid by seller, buyer normally reimburses seller: buyer debit, seller credit.
- Saying the estimate factor must mathematically come first Applying 1.05 to the full base or to its unrounded time share gives the same result. Early rounding or applying the wrong factor causes errors.
- Confusing a tax credit with payment to the county The credit reallocates responsibility; identify who actually pays the bill.
- Automatically reimbursing uncollected rent Read the assignment, collectability and settlement terms. Do not invent a guaranteed buyer collection.
- Prorating a refundable deposit as though it were rent Use the stated transfer liability and applicable law, separately from earned income.
- Adding an unpaid-bill credit after the bill was paid directly Record that economic payment once; distinguish separate tax years and amounts.
Check your understanding
These are original teaching questions, not recalled or predicted PSI questions. Answer first, then explain why the other choices fail.
1. An unpaid $7,300 annual expense uses 365 days and 90 seller days. Buyer will pay it later. What adjustment applies?
- $2,000 seller debit and buyer credit
- $657 seller credit and buyer debit
- $1,800 seller debit and buyer credit
- $1,825 seller credit and buyer debit
Show answer and explanation
Answer: C. $1,800 seller debit and buyer credit
$7,300 / 365 x 90 = $1,800. Because buyer will pay the seller-period expense, debit seller and credit buyer.
2. Seller prepaid $1,200 annual dues. Under whole-month allocation, buyer owns October through December. What adjustment applies?
- $1,200 buyer credit only
- $900 seller credit and buyer debit
- $300 seller credit and buyer debit
- $300 seller debit and buyer credit
Show answer and explanation
Answer: C. $300 seller credit and buyer debit
Three buyer months at $100 each give $300. Buyer reimburses seller: seller credit and buyer debit.
3. Seller collected $3,100 July rent. Actual-day allocation gives buyer July 11 through 31. What does buyer receive?
- $3,100 credit
- $1,000 credit
- $2,000 debit
- $2,100 credit
Show answer and explanation
Answer: D. $2,100 credit
Buyer has 21 of 31 days. $3,100 / 31 x 21 = $2,100. Seller already collected the buyer-period rent, so debit seller and credit buyer.
4. Using actual days over 365 in 2026, buyer gets June 15. How many days belong to seller from January 1?
- 165
- 180
- 166
- 164
Show answer and explanation
Answer: A. 165
January 31 + February 28 + March 31 + April 30 + May 31 + June 14 = 165. Closing day is excluded from seller time.
5. A stated 30/360 calculation gives seller four 30-day months plus 15 days. How many responsible units apply?
- 135
- 137
- 145
- 120
Show answer and explanation
Answer: A. 135
4 x 30 + 15 = 135. This uses the expressly stated synthetic month convention, not actual calendar months.
6. A contract uses 105% of an $8,000 prior annual tax bill. What estimated annual base applies?
- $8,105
- $8,400
- $8,000
- $7,619.05
Show answer and explanation
Answer: B. $8,400
$8,000 x 1.05 = $8,400. That is a contractual estimate, not a guaranteed official future bill.
7. A problem explicitly uses actual 366-day allocation in 2028 and gives buyer March 1. What is seller's share of $7,320 for January and February?
- $1,220
- $1,200
- $1,203.29
- $1,180
Show answer and explanation
Answer: B. $1,200
January 31 plus February 29 gives 60 days. $7,320 / 366 x 60 = $1,200. Do not use 365 when this problem expressly chooses 366.
8. The instructions transfer a $2,500 refundable deposit to buyer, who also receives $1,800 buyer-period rent already held by seller. Which is correct?
- Debit seller and credit buyer $4,300, with separate labels
- Prorate $2,500 by the seller's rental days
- Treat the full $4,300 as seller-earned rent
- Credit seller $4,300 as prepaid expense
Show answer and explanation
Answer: A. Debit seller and credit buyer $4,300, with separate labels
The deposit is a separate tenant-related liability and the rent is buyer-period income. Both specified amounts flow toward buyer, but the full deposit is not allocated as earned daily rent.
9. A prior $7,200 bill is adjusted by 1.05 and allocated for 100 days over 360. Which calculation is equivalent before rounding?
- ($7,200 / 360 x 100) x 1.05
- $7,200 / 360 x 100 + 1.05
- $7,200 / 100 x 360 x 1.05
- $7,200 / 1.05 / 360 x 100
Show answer and explanation
Answer: A. ($7,200 / 360 x 100) x 1.05
Multiplication by 1.05 can be applied to the original base or the unrounded time share. Both valid orders give $2,100. This does not justify early rounding or changing the contractual factor.
10. A prior-year $8,000 bill is paid directly from seller's proceeds at closing. A separate current-year seller share of $2,000 remains for buyer to pay later. Which buyer credit follows those facts?
- $2,000
- $8,000
- $6,000
- $10,000
Show answer and explanation
Answer: A. $2,000
Only the separate $2,000 seller share remains for buyer to pay. The $8,000 direct payment is already accounted for and must not also be credited to buyer as an unpaid bill.
Common questions
What is the proration formula?
Divide the full-period amount by the specified period units, then multiply by the responsible units. A $7,300 annual expense over 365 days is $20 a day. Ninety responsible days produce a $1,800 share. Payment status determines which party gets the debit or credit.
How do I tell a seller debit from a seller credit?
Ask who must reimburse whom. A seller debit reduces seller proceeds; a seller credit increases them. If buyer will pay an unpaid expense for seller time, seller normally receives a debit and buyer a matching credit. A seller-prepaid buyer benefit reverses the entries.
Who gets closing day for a proration?
Use the party and adjustment date stated in the question or contract. Buyer gets closing day means seller time ends the day before. Seller gets closing day means include it in seller time. A possession-based adjustment date can differ from closing; there is no universal assignment supplied by this page.
Does every 360-day calculation use 30-day months?
No. A named 30/360 method and an Actual/ 360 method share a denominator but use different day counts. Fannie Mae's cited multifamily interest guidance expressly distinguishes them. Its servicing default is not an Illinois tax-proration default. Follow the convention supplied for the question.
When do I use 365 or 366 days?
Use the stated denominator and day-count method. An actual-year allocation uses 365 days in 2026 or 366 in a leap year such as 2028. Do not silently replace an express Actual/ 365 loan convention with an actual-year convention. A monthly rent problem may instead use the actual days in that month.
How are Illinois property taxes handled at closing?
IDOR says existing-home sellers generally pay outstanding bills and provide a credit for their ownership period under the real estate contract; buyers generally pay bills due after closing. Identify the tax year, payment status and contract estimate. Illinois's usual assessment-and-billing cycle spans two years, so a bill payable this year can relate to last year.
Does Illinois always require 105% tax proration?
No statewide 105% rule is established by the cited IDOR guidance. Use the factor actually given in the contract or exam question. A factor estimates the base; it does not determine the final tax assessment, exemptions, rate or bill.
Must I apply the tax estimate factor before counting the seller share?
Building the annual base first is easy to follow, but it is not the only correct order. Before rounding, multiplying the bill by its estimate factor before prorating gives the same result as multiplying its calculated time share by that factor. Keep the factor and bases correct and avoid rounding intermediate amounts.
Is a seller tax credit the same as paying the tax collector?
No. The credit reallocates money between the parties. The bill still needs to be paid by whoever is responsible under the transaction. Do not add a buyer credit for a full bill that the settlement agent already pays directly from seller funds. Separate tax years can require separate amounts.
Is lender tax escrow the same as tax proration?
No. A lender reserve sets aside funds for future bills. A seller tax adjustment reallocates expense between buyer and seller. IDOR identifies the lender reserve as a separate possible closing requirement. Read the settlement entries together without treating every separate reserve as an accounting duplicate.
How is rent collected before closing prorated?
For rent the seller collected covering buyer time, calculate the buyer-period share using the stated monthly or daily convention. Normally debit seller and credit buyer that amount. The balance for seller time remains seller income under the given arrangement.
What about rent earned but not collected?
Do not assume buyer will collect it or guarantee it. The contract may assign arrears, require an agreed closing adjustment or account for them only when collected. Use the question's collection and reimbursement facts before entering a seller credit and buyer debit.
Do refundable security deposits get prorated by days?
No. A refundable deposit is a tenant-related liability. Record the stated transferred amount separately from earned rent. Under 765 ILCS 710/1.1, in a covered residential transfer other than to a lien-interest holder, transferee liability includes the deposit, statutory interest or prepaid rent paid to the transferor; transferor remains jointly and severally liable. A private closing credit does not erase that liability.
Can I prorate the seller's insurance policy automatically?
No. Read whether the buyer actually receives the prepaid benefit. The CFPB's Closing Disclosure interpretation gives flood and hazard premiums as an adjustment example when the consumer is substituted as an insured under the same policy. A seller cancellation refund and a separate new buyer policy are different facts.
Is reproration automatic when an estimate differs from the final bill?
Do not assume that. Read the agreement's finality, later-adjustment and payment terms and applicable law. IDOR notes that new-construction transactions often use a tax reproration agreement. A later correction, if required, is separate from the original estimate.
How do these items appear on a Closing Disclosure?
For covered transactions, Regulation Z 1026.38 provides paired transaction adjustments for seller-paid-in-advance items and seller-unpaid items. Advance rent can also appear as an adjustment. The form reports the transaction; its headings do not choose the parties' tax-proration factor or override the contract.
How should I round and check the shares?
Keep the daily rate unrounded until the requested final step. For a calendar allocation of one fixed period amount, compare the combined unrounded buyer and seller shares with the total. Independently rounding both shares can create a penny difference; reconcile it as instructed. Do not alter the actual day count to hide it.
Are these official exam questions or guaranteed settlement instructions?
No. They are original examples with explicit facts and do not replace an actual contract, lease, title or settlement review. Your practice result identifies topics to revisit; it is not a validated passing prediction.
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Official sources and scope
Checked October 25, 2026. The PSI outline and relevant IDOR and CFPB provisions were read. The complete cited Fannie Mae day-count paragraphs and Illinois deposit-transfer section were read through official indexed text; direct retrieval returned errors. Their stated scopes are preserved. The earlier general tax study and forms guide were not carried as supposedly checked authorities. Original examples do not determine an actual settlement.
- PSI June 24, 2026 outline: real property tax and other prorations
- IDOR: seller property-tax responsibility at closing
- IDOR: property-tax assessment and billing cycle
- CFPB Regulation Z 1026.38: paired closing adjustments
- Fannie Mae: Actual/ 360 and 30/360 definitions
- 765 ILCS 710/1.1: residential transferee liability
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.