Real estate proration problems: 360 vs 365 days, closing day and who gets the credit

The 4-step proration method

A proration splits a cost that covers a period of time between the seller and the buyer, so each pays only for the days they own the property. PSI's content outline for the salesperson exam lists "real property tax and other prorations" under Real Estate Calculations, the math area worth 7% of the test. Every proration question, whether it is taxes, rent or interest, falls to the same four steps.

1. Find the amount and the period it covers. Annual taxes cover a year. Rent usually covers one month. Loan interest covers the month before the payment date.
2. Find the daily rate. Divide the amount by the days in the period, using the day count the question names: 360 days a year with 30-day months, or the actual days (365 in a normal year).
3. Count the days you need. Decide whose share you are calculating, check who owns the closing day, and count from the right start date to the right end date.
4. Multiply and assign. Daily rate times days gives the proration. Then decide who gets the debit and who gets the credit, which depends on whether the cost was paid in advance or is unpaid (in arrears).

Count only the share you need. If the seller owes for the days already used, calculate the seller's days. If the seller paid ahead, calculate the buyer's days, because that is what the buyer pays back. Calculating the other party's share is the most common way to land on a wrong answer choice that looks right.

For the full formula sheet, see the real estate math study guide or the printable NJ real estate math formulas.

Arrears vs prepaid: who gets the credit

This is the step that decides the direction of the money, and it is where most points are lost. Ask one question: has the cost for this period already been paid?

The federal Closing Disclosure uses the same logic in plain words. Its summaries of the transaction have one block called "Adjustments for Items Paid by Seller in Advance", which is due from the borrower and due to the seller, and another called "Adjustments for Items Unpaid by Seller", which is credited to the borrower and charged to the seller. City and town taxes, county taxes and assessments are the standard lines in both.

360-day vs 365-day: the two day-count conventions

The question will tell you which year to use. If it says "use a 360-day year" or "a statutory year" or "banker's year", every month counts as 30 days and a year is 360. If it says "use a 365-day year" or "actual days", count the real calendar days in each month.

The two methods give slightly different answers, and PSI-style questions often put both results in the answer choices. That is why you read the convention before you touch a number. A quick way to count days on a 360-day year: number of full months times 30, plus the day of the current month.

Leap years: with actual days, some problems divide by 366 in a leap year. If the question says to use a 365-day year, use 365 even in a leap year. Follow the wording.

Round at the end, not in the middle. In the first example below, dividing $7,200 by 365 gives about $19.7260 a day. Using the full rate for 166 days gives $3,274.52. Rounding the daily rate to $19.73 first gives $3,275.18. The gap is small, but answer choices can be that close. If no choice matches exactly, pick the closest one; question writers sometimes round the daily rate first.

Who owns the closing day

Someone has to be charged for the day of closing, and real estate textbooks and exam questions do not all agree on who. The question will tell you, usually with wording like "the seller is responsible for the day of closing" or "the buyer owns the day of closing." Textbooks differ on this, so there is no safe default to fall back on. Reread the stem for the closing-day wording before you count a single day.

• Seller owns the closing day: the seller's days run from the start of the period through the closing date. The buyer's days start the day after closing.
• Buyer owns the closing day: the seller's days run through the day before closing. The buyer's days start on the closing date.

Switching the closing day moves exactly one day's worth of money. In the examples below, that is $20 a day on a 360-day year, so a wrong assumption costs you the question even when everything else is right.

Six worked examples

Each example is computed exactly, with the result rounded to the cent at the end. Names are illustrative. Dates are in 2026 and 2027, which are not leap years.

Example 1: taxes in arrears, both conventions. Annual taxes on Dana's house are $7,200 and nothing has been paid for the year. She closes on June 15, and the seller owns the closing day. Dana owes for January 1 through June 15.

• 360-day year: $7,200 / 360 = $20.00 a day. Days: 5 full months x 30 = 150, plus 15 = 165. 165 x $20.00 = $3,300.00.
• 365-day year: $7,200 / 365 = $19.7260 a day. Days: 31 + 28 + 31 + 30 + 31 + 15 = 166. 166 x $19.7260 = $3,274.52.
• Entry: the taxes are unpaid, so debit the seller and credit the buyer. The difference between the two methods is $25.48.

Example 2: same house, but the buyer owns the closing day. The seller's days now end on June 14.

• 360-day year: 5 x 30 = 150, plus 14 = 164 days. 164 x $20.00 = $3,280.00.
• 365-day year: 166 - 1 = 165 days. 165 x $19.7260 = $3,254.79.
• Entry: still a seller debit and a buyer credit. Moving the closing day changed the answer by one day's tax.

Example 3: taxes paid in advance. Omar already paid the full year's taxes of $8,760. He sells to Kim, closing September 20, and Omar owns the closing day. Use a 365-day year.

• Daily rate: $8,760 / 365 = $24.00.
• Kim's days, September 21 through December 31: 10 + 31 + 30 + 31 = 102.
• 102 x $24.00 = $2,448.00. Omar prepaid, so credit the seller and debit the buyer $2,448.00.

Example 4: rent collected in advance. Rosa owns a rental and collected October rent of $2,480 on October 1. She closes on October 12, and the buyer owns the closing day.

• Actual days: October has 31 days, so $2,480 / 31 = $80.00 a day. Buyer's days, October 12 through 31: 20. 20 x $80.00 = $1,600.00.
• 30-day month: $2,480 / 30 = $82.6667 a day. Buyer's days, October 12 through 30 (day 31 does not exist in this convention): 19. 19 x $82.6667 = $1,570.67.
• Entry either way: Rosa collected money for days the buyer will own, so debit the seller and credit the buyer.

Example 5: interest on an assumed loan. Ben is assuming the seller's loan. The balance is $240,000 at 6% after the August 1 payment, which covered July's interest. Closing is August 17, and the seller owns the closing day. Use a 360-day year.

• Annual interest: $240,000 x 0.06 = $14,400. Daily: $14,400 / 360 = $40.00.
• Seller's days, August 1 through 17: 17. 17 x $40.00 = $680.00.
• Interest is paid in arrears, so the September 1 payment Ben makes will include those 17 days. Debit the seller and credit the buyer $680.00. On a 365-day year the same proration would be $670.68.

Example 6: prepaid interest on a new loan. Ana takes a new $320,000 loan at 6.75%, closing March 20, 2027, with her first payment due May 1. That May payment covers April's interest, so the lender collects interest for March 20 through March 31 at closing. The question says to count the closing day and use a 365-day year.

• Annual interest: $320,000 x 0.0675 = $21,600. Daily: $21,600 / 365 = $59.1781.
• Days, March 20 through 31: 12. 12 x $59.1781 = $710.14.
• Entry: this is a buyer debit only. The seller is not part of it, so there is no matching seller credit. On a 360-day year it would be $720.00.

The Consumer Financial Protection Bureau describes prepaid interest the same way: daily interest from the date you close until the period covered by your first monthly payment, shown in section F of the Loan Estimate and Closing Disclosure.

Rent and interest prorations, briefly

Rent is almost always paid in advance, at the start of the month. If the seller collected it, the buyer gets a credit for the days the buyer will own. The daily rate comes from that month: divide by its actual days, or by 30 if the question uses 30-day months. Do not divide monthly rent by 365.

Mortgage interest is paid in arrears. A payment due on the first of a month pays the previous month's interest. That is why a buyer who assumes a loan gets a credit for the seller's days in the current month, and why a buyer with a new loan pays prepaid interest from closing to the end of the month.

How property taxes work in New Jersey

Exam problems usually give you an annual tax and tell you whether it is paid. Real New Jersey tax bills are quarterly. For towns on a calendar fiscal year, N.J.S.A. 54:4-66 makes taxes payable in four installments due February 1, May 1, August 1 and November 1. The first two installments are generally one-quarter of the previous year's total tax, and the last two make up the rest of the current year's tax, as the state Division of Local Government Services guide to the statute explains.

So in a real New Jersey closing, the seller has often paid some installments and not others. On the exam, do not guess at local practice. Use only what the question gives you: the amount, what has been paid, the day-count convention and who owns the closing day.

Doing prorations on test day

PSI's bulletin lists handheld calculators among the prohibited devices and does not describe a provided calculator, so practice prorations by hand. At a test center you get a piece of scratch paper and a pencil. Remote candidates are not allowed scratch paper, which makes multi-step math harder to track; factor that in when you choose how to test.

• Underline three things before calculating: the day-count convention, who owns the closing day, and whether the item is paid or unpaid.
• Write the daily rate first, then the day count, then multiply.
• Check the direction last. Find the choice with your number and the right debit and credit.
• Sanity check: a June closing should split annual taxes roughly in half. If your seller share is more than the whole year, you counted wrong.

Our suggestion: work a set of mixed problems until the four steps are automatic. The math practice drills and the real estate math hub cover prorations alongside the other calculation types, and a full practice exam tells you whether math is where you are losing points.