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Real estate mathematics 13 min read

Closing Prorations, Day Counts, Debits and Credits

A closing proration divides an expense or income item between seller and buyer for their respective time periods. First find the daily or monthly rate, then multiply by the number of days or months assigned to the responsible party. An item paid in advance commonly creates a buyer debit and seller credit for the buyer's period. An unpaid item commonly creates a seller debit and buyer credit for the seller's period. Follow the contract and the problem's closing-day rule.

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What this guide does

It explains the curriculum concept, applies it to New York scenarios and links the primary material used for regulated or date-sensitive claims. It is independent exam preparation, not legal, tax, lending, appraisal or eligibility advice.

The arithmetic is only half the task. You must also decide who benefited, who paid or will pay, and which party needs reimbursement.

What are the core proration formulas?

FindFormula
Daily rate using a stated 365-day yearAnnual amount ÷ 365
Daily rate using a stated 360-day yearAnnual amount ÷ 360
Daily rate for a stated billing periodPeriod amount ÷ Actual days in that period
Monthly rateAnnual amount ÷ 12
Prorated amountRate per period × Number of periods assigned
Remaining advanceAmount paid - Amount used before closing

Do not select 360, 365 or actual days from habit. Use the method the question, contract or closing instruction supplies.

Official source map

The New York State Department of State 77-hour curriculum includes Closing Costs and Adjustments under Title and Closing. It expressly lists taxes, assessments, insurance, fuel, water and sewer charges, rent, security deposits and the arithmetic of prorations. Credits, debits and proration are key terms.

The Department of State salesperson page says the multiple-choice examination is based on the curriculum and allows 1 1/2 hours after instructions. It does not publish an official proration-question count or subject weighting.

The Consumer Financial Protection Bureau's current Closing Disclosure rule provides for adjustments involving prepaid or unpaid taxes, assessments and other items. Its official interpretation gives examples including tax and association-fee prorations, unpaid utilities, advance rent and interest on loan assumptions.

The CFPB's Closing Disclosure explainer distinguishes items paid by the seller in advance from items left unpaid by the seller. These disclosure rules identify categories and presentation. The purchase contract, applicable law and actual transaction facts determine responsibility.

What is a proration?

A proration allocates one item across time. The purpose is to charge each party for the period assigned to that party or reimburse a party who paid for another party's period.

Common items include:

  • real property taxes and assessments
  • association charges
  • rent
  • utilities and water charges
  • fuel remaining at the property
  • insurance in a transaction where an adjustment applies
  • interest on an assumed loan

Not every closing uses every adjustment. Use only the items stated in the problem.

What do debit and credit mean at closing?

In simplified settlement math:

  • a debit increases what a party owes or reduces what that party receives
  • a credit reduces what a party owes or increases what that party receives

For a two-party reimbursement, one party's debit commonly matches the other party's credit.

Example 1: Paid-in-advance item

The seller paid an annual charge that covers a period after title transfers. The buyer will receive the benefit during the buyer's period.

The buyer reimburses the seller:

  • buyer: debit
  • seller: credit

Example 2: Unpaid accrued item

The seller used a service or owned during a tax period, but the buyer will pay the bill later.

The seller reimburses the buyer at closing:

  • seller: debit
  • buyer: credit

Do not memorize the columns without the reason. Ask who paid, who will pay and whose period the amount covers.

Who owns the day of closing?

Use the rule stated in the problem or contract. A question may assign the closing day to the buyer or seller. That choice changes the day count by one.

A New York Department of Taxation and Finance opinion discussing tax apportionment notes that closing attorneys commonly agree on allocation, with the purchaser liable from the date of title transfer in the situation discussed. That does not create a shortcut for every educational question or every item.

Write one sentence before counting:

Buyer owns closing day.

Or:

Seller owns closing day.

Then count consistently.

How do you count calendar days?

For an actual-calendar problem, use the number of days in each month.

MonthDays in 2026
January31
February28
March31
April30
May31
June30
July31
August31
September30
October31
November30
December31

The year 2026 is not a leap year. For another year, check whether February has 28 or 29 days.

Example 3: Buyer owns closing day

Closing is April 10, and the buyer owns the closing day. For an item beginning April 1:

  • seller period: April 1 through April 9 = 9 days
  • buyer period: April 10 through April 30 = 21 days

The two periods total 30 days.

Example 4: Seller owns closing day

Using the same April 10 closing:

  • seller period: April 1 through April 10 = 10 days
  • buyer period: April 11 through April 30 = 20 days

The total remains 30 days, but one day moves between the parties.

How does a 360-day year work?

Some educational problems direct students to use twelve 30-day months:

Annual amount ÷ 360 = Daily rate

Example 5

An annual item is $9,000. The problem requires a 360-day year.

Daily rate = $9,000 ÷ 360 = $25

For 72 assigned days:

Proration = $25 × 72 = $1,800

Do not substitute 365 when the problem says 360.

How does a 365-day year work?

Use:

Annual amount ÷ 365 = Daily rate

Example 6

Annual taxes are $7,300. The problem requires a 365-day year.

Daily rate = $7,300 ÷ 365 = $20

For 108 assigned days:

Proration = $20 × 108 = $2,160

The same annual amount would produce a different daily rate under a 360-day convention.

How do you prorate prepaid taxes?

If the seller paid taxes covering the buyer's ownership period, calculate the buyer's share. The buyer reimburses the seller.

Example 7: Seller paid, buyer owns closing day

Facts:

  • annual tax: $7,300
  • use a 365-day year
  • buyer's assigned period: 108 days
  • seller paid the tax in advance

Daily rate = $7,300 ÷ 365 = $20

Buyer's share = $20 × 108 = $2,160

Entry:

  • buyer debit: $2,160
  • seller credit: $2,160

The debit does not mean the buyer pays the taxing authority twice. It reimburses the seller for the buyer's allocated period under the stated facts.

How do you prorate unpaid taxes?

If the taxes remain unpaid and the buyer will pay them later, calculate the seller's share. The seller reimburses the buyer at closing.

Example 8

Facts:

  • annual tax: $10,950
  • use a 365-day year
  • seller's assigned period: 140 days
  • buyer will pay the full bill later

Daily rate = $10,950 ÷ 365 = $30

Seller's share = $30 × 140 = $4,200

Entry:

  • seller debit: $4,200
  • buyer credit: $4,200

How do you prorate a monthly charge?

Use the stated month length or the method supplied.

Example 9: Association charge paid in advance

A $930 April association charge was paid by the seller. Closing is April 19, the buyer owns the closing day, and the problem uses actual days.

Buyer owns April 19 through April 30:

Buyer days = 12

Daily rate = $930 ÷ 30 = $31

Buyer reimbursement = $31 × 12 = $372

Entry:

  • buyer debit: $372
  • seller credit: $372

How do you prorate rent collected in advance?

If the seller collected rent covering the buyer's ownership period, the seller holds income attributable to the buyer. The usual simplified entry is a seller debit and buyer credit.

Example 10

Monthly rent is $3,000 for a 30-day month. The seller collected it in advance. Closing is on the 21st, and the buyer owns the closing day.

Buyer period is day 21 through day 30, or 10 days.

Daily rent = $3,000 ÷ 30 = $100

Buyer's rent share = $100 × 10 = $1,000

Entry:

  • seller debit: $1,000
  • buyer credit: $1,000

How do you handle accrued but uncollected rent?

If the buyer will later collect rent earned during the seller's period, the buyer will receive money attributable to the seller. In a simplified two-party problem, the buyer reimburses the seller at closing.

Example 11

Rent is $2,400 for a 30-day month. The buyer will collect the full amount after closing. The seller is assigned the first 18 days.

Daily rent = $2,400 ÷ 30 = $80

Seller's earned share = $80 × 18 = $1,440

Entry:

  • buyer debit: $1,440
  • seller credit: $1,440

How is a security deposit treated?

A tenant security deposit is not rental income. It is money held subject to an obligation to the tenant. When the buyer assumes that obligation, the settlement must account for the deposit as required by the transaction and applicable law.

In a simplified problem where the seller transfers responsibility for a $4,000 deposit to the buyer:

  • seller debit: $4,000
  • buyer credit: $4,000

This gives the buyer the funds associated with the obligation. Do not prorate the deposit by days unless the question supplies a special reason.

How do you adjust fuel or supplies on hand?

Fuel remaining in a tank is an inventory-style adjustment, not a time proration. Multiply the verified quantity by the stated unit price.

Example 12

At closing, 240 gallons of fuel remain. The agreed price is $3.25 per gallon, and the seller paid for the fuel.

240 × $3.25 = $780

Entry:

  • buyer debit: $780
  • seller credit: $780

The buyer receives the remaining fuel and reimburses the seller under the stated agreement.

How do prorations appear on a Closing Disclosure?

The CFPB rule provides separate summaries for the consumer and seller and identifies adjustments for items paid by the seller in advance or left unpaid by the seller. The disclosure can include city or town taxes, county taxes, assessments and additional applicable items.

Avoid assuming every classroom “debit” will appear under that exact word on every modern form. Understand the economic direction, then follow the form and labels supplied.

The CFPB also distinguishes total closing costs from cash to close. A proration can change the cash due, but it is not another name for the entire closing-cost total.

What are the common proration mistakes?

Counting the closing day twice or not at all

Assign it to one party according to the problem, then confirm the two day counts total the full period.

Choosing 360 or 365 without instruction

Use the stated convention. If none is supplied and the result depends on it, the educational item lacks a necessary fact.

Prorating the wrong party's period

For a prepaid item, usually find the other party's benefiting period. For an unpaid item, usually find the period attributable to the party who will not pay the later bill.

Reversing debit and credit

Ask who must reimburse whom. The reimbursing party receives the debit; the party being reimbursed receives the credit in a simple two-party entry.

Treating security deposits as income

They are held subject to an obligation and require transfer accounting, not ordinary rent proration.

Mixing annual and monthly amounts

Match the rate to the time unit before multiplying.

Rounding the daily rate too early

Keep the full calculator value and round the final money amount unless the problem instructs otherwise.

What is a reliable exam-day workflow?

  1. Identify the item and coverage period.
  2. Determine whether it is paid, unpaid, collected in advance or to be collected later.
  3. Write who owns the closing day.
  4. Choose the stated 360-day, 365-day or actual-day method.
  5. Count the responsible party's days.
  6. Calculate the rate and prorated amount.
  7. Decide who reimburses whom.
  8. Label the buyer and seller debit or credit.
  9. Check that the day counts cover the entire period once.

Review the New York real estate math formula map and the Real Estate Mathematics study guide for the related percentage, tax and finance formulas.

Can you solve these original practice questions?

Practice 1

An annual charge is $8,760. A problem uses a 365-day year and assigns 75 days to the buyer. What is the buyer's share?

A. $1,440
B. $1,800
C. $2,400
D. $6,960

Answer: B. The daily rate is $8,760 ÷ 365 = $24. The share is $24 × 75 = $1,800.

Practice 2

The seller paid a charge in advance. The buyer's allocated share is $925. What is the simplified entry?

A. Buyer debit, seller credit
B. Buyer credit, seller debit
C. Debit both parties
D. Credit both parties

Answer: A. The buyer reimburses the seller for the buyer's period.

Practice 3

Unpaid taxes will be paid later by the buyer. The seller's allocated share is $3,600. What is the simplified entry?

A. Buyer debit, seller credit
B. Buyer credit, seller debit
C. Buyer debit only
D. Seller credit only

Answer: B. The seller reimburses the buyer for the seller's period.

Practice 4

Rent is $2,700 for a 30-day month. The seller collected it in advance. The buyer owns the final 12 days. What amount belongs to the buyer?

A. $900
B. $1,080
C. $1,620
D. $2,700

Answer: B. Daily rent is $2,700 ÷ 30 = $90. The buyer's share is $90 × 12 = $1,080.

Practice 5

Closing is June 16, and the buyer owns the closing day. How many June days belong to the seller?

A. 14
B. 15
C. 16
D. 30

Answer: B. The seller owns June 1 through June 15, or 15 days.

Practice 6

An annual item is $10,800. The problem requires a 360-day year. What is the daily rate?

A. $29.59
B. $30
C. $36
D. $45

Answer: B. $10,800 ÷ 360 = $30 per day.

Practice 7

There are 175 gallons of fuel on hand at $3.60 per gallon. What adjustment amount is indicated?

A. $486
B. $525
C. $630
D. $648

Answer: C. 175 × $3.60 = $630.

Practice 8

Which statement is accurate?

A. A security deposit is advance rent earned by the seller.
B. Every New York proration uses a 360-day year.
C. A paid-in-advance item can require the buyer to reimburse the seller.
D. The seller owns the closing day in every transaction.

Answer: C. The day-count method and closing-day assignment come from the stated facts, and a security deposit remains tied to an obligation.

Frequently asked questions

What is a closing proration?

It is an allocation of an expense or income item between parties according to their assigned periods or responsibility.

Should I use a 360-day or 365-day year?

Use the convention stated in the question or controlling closing instruction. The two methods can produce different results.

Who gets the day of closing?

Follow the problem or contract. Assign the closing day to one party and count the rest of the period consistently.

What is the difference between a debit and a credit?

A debit increases what a party owes or reduces proceeds. A credit reduces what a party owes or increases proceeds.

How are prepaid taxes adjusted?

When the seller paid taxes covering the buyer's period, the buyer commonly reimburses the seller with a buyer debit and seller credit.

How are unpaid taxes adjusted?

When the buyer will pay taxes attributable partly to the seller's period, the seller commonly gives the buyer a credit for the seller's share.

Is advance rent handled like a security deposit?

No. Advance rent is income allocated by rental period. A security deposit is held subject to an obligation to the tenant.

Does New York publish an official proration-question count?

No. The curriculum includes proration arithmetic, debits and credits, but the Department of State does not publish a topic-level question count or weighting.

Sources and verification notes

This article was checked against official sources available on August 27, 2026. Every example states the assumptions needed for its calculation and is original exam-preparation content.

Use this lesson for education and exam preparation. Actual adjustments must follow the contract, applicable law, bills, title documents and closing professionals' calculations.

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