Real estate proration math
360-day versus 365-day proration: choose both parts of the method
For an annual charge, proration equals the annual amount multiplied by the responsible days and divided by the stated year basis. A 30/360 question uses assumed 30-day months and a 360-day year. An Actual/365 question uses calendar days and 365. Read both parts: Actual/360 also exists, so a 360 denominator alone does not prove that every month has 30 days.
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What do 30/360, Actual/365 and Actual/360 mean?
| Stated method | Responsible-day count | Year denominator |
|---|---|---|
| 30/360 | Assumed 30-day months, with the specified partial-month and month-end rules | 360 |
| Actual/365 | Actual calendar days in the assigned period | 365 |
| Actual-year method within a leap year, when directed | Actual calendar days, including February 29 when within the period | 366 |
| Actual/360, when directed | Actual calendar days | 360 |
Fannie Mae's multifamily servicing guide, 204.02A and B, distinguishes Actual/360 interest from 30/360 interest. That is a counterexample to the claim that a 360 denominator always requires 30-day months. Its loan-servicing rules do not establish the method for every Illinois tax proration or broker exam question.
The annual-charge examples below state their methods. A supplied day count can be used directly; a date range must first be counted under its convention. A monthly charge allocated over an actual month needs that month's period, not an annual denominator automatically copied from a different problem. Write the full-period amount, its period, the day-count rule and who is responsible for closing day before calculating.
A useful calculation order
- Identify the charge or income and the period it covers.
- Write the assigned start date, end date and closing-day rule.
- Count days under the stated convention.
- Calculate amount × responsible days ÷ denominator without early rounding.
- Choose the entry from who paid, who benefited and who will pay later.
Worked comparison: the same bill and closing date
Assume a fictional $7,300 annual tax amount for calendar year 2026. Closing is March 10, and the buyer is responsible for closing day. The seller's period is January 1 through March 9. No estimated tax factor, separate prior-year balance or other adjustment is included.
| Step | Simplified 30/360 instructions | Actual/365 instructions |
|---|---|---|
| Seller days | January 30 + February 30 + March 9 = 69 | January 31 + February 28 + March 9 = 68 |
| Unrounded daily rate | $7,300 ÷ 360 = $20.277777… | $7,300 ÷ 365 = $20 |
| Seller share | $7,300 × 69 ÷ 360 = $1,399.17 after rounding | $7,300 × 68 ÷ 365 = $1,360 |
| Buyer days, for this same full-year allocation | 360 minus 69 = 291 | 365 minus 68 = 297 |
| Buyer share | $7,300 × 291 ÷ 360 = $5,900.83 after rounding | $7,300 × 297 ÷ 365 = $5,940 |
Each pair of shares totals $7,300. The seller's amounts differ by $39.17 because both the day count and the denominator differ. Comparing methods does not mean keeping one method's day count and silently changing only its denominator.
Change the closing-day rule: under the Actual/365 example, if the seller is responsible through March 10, the seller count becomes 69 and the share becomes $1,380. Buyer days become 296. Count closing day once, not twice or zero times.
For a different comparison that expressly supplies 75 days under each method, $18,000 × 75 ÷ 360 is $3,750, while $18,000 × 75 ÷ 365 is $3,698.63. That isolates the denominator effect. It does not establish that a particular date range contains 75 days under both conventions.
Which side gets the debit or credit?
The amount is only one part of the answer. Identify whether the item is an expense already paid, an unpaid expense or income collected for someone else's period. The word prepaid alone is not enough.
| Facts | Seller entry | Buyer entry |
|---|---|---|
| Unpaid seller-period tax that the buyer will pay later | Debit | Credit |
| Seller already paid an expense for the buyer's period, and buyer must reimburse it | Credit | Debit |
| Seller collected tenant rent in advance for the buyer's post-closing period | Debit | Credit |
12 CFR 1026.38(j) and (k) separately address prepaid and unpaid adjustments on a covered Closing Disclosure. The commentary to (j)(2)(vi) also addresses rent collected by the seller for a period after closing. These disclosure rules do not make every insurance policy transferable or supply one universal closing-day or tax-factor agreement.
For example, assume the buyer will later pay the unpaid $1,360 seller share from the Actual/365 example. Debit the seller and credit the buyer $1,360. That credit is a settlement adjustment, not a statement that the tax authority has already been paid.
How much can early rounding change the answer?
Keep the unrounded daily rate in the calculation and round the final money amount to cents unless instructed otherwise. For $8,765 over 365 days with a 200-day responsibility period:
- Unrounded calculation: $8,765 × 200 ÷ 365 = $4,802.739726…
- Final amount: $4,802.74.
- Rounding the daily rate to $24.01 first gives $24.01 × 200 = $4,802.00, which is $0.74 lower.
Enter the multiplication and division as one calculation when possible. If separately rounded shares leave a cent difference in another example, reconcile it under the stated rounding and allocation instructions. Do not change a correct day count to force agreement. For a real closing, verify the settlement agent's treatment.
What does this mean for Illinois property-tax closings?
The Illinois Department of Revenue's closing guidance says sellers of existing homes generally pay outstanding tax bills and credit buyers for the seller's ownership period under the contract. Buyers generally pay bills due after closing. New-construction tax allocation and later reproration also depend on the agreement.
A prior bill, estimated tax factor, exemption change or separate unpaid installment can change the full transaction calculation. Use the amount and instructions supplied in an exam example. Do not substitute an assumed 105% factor, treat an estimate as a final tax bill or count the same outstanding bill twice. This page's fictional calculations do not decide a private tax allocation or loan-interest obligation.
Try six original proration questions
Choose before opening the explanation. These are original study calculations, not released or recalled PSI items.
1. The instruction expressly says Actual/360
A calculation supplies actual calendar days and a 360-day year basis. Which setup follows it?
- Replace every calendar month with 30 days automatically
- Change the denominator to 365
- Reject the instruction because actual days can never use 360
- Use the actual responsible days with the stated 360 denominator
Show answer 1
D is correct. A changes the numerator convention. B changes the denominator. C mistakes Actual/360 for an inherently invalid mix. D follows both stated parts.
Change the fact: the problem instead specifies 30/360. Use its 30-day-month and partial-month instructions, not the former actual-calendar count.
2. The buyer gets March 10
Use the fictional $7,300 annual bill, 2026, Actual/365 and seller responsibility from January 1 through March 9. What is the seller share?
- $1,399.17
- $1,360
- $1,380
- $5,940
Show answer 2
B is correct. A is the separate 30/360 result. B uses 68 actual days at $20 per day. C adds closing day to the seller. D is the buyer's remaining-year share.
Change the fact: seller responsibility includes March 10. The Actual/365 share becomes 69 × $20 = $1,380.
3. Closing moves to April 10
For a nonleap actual-calendar year, the seller is responsible January 1 through the day before April 10. How many seller days are there?
- 99
- 100
- 90
- 101
Show answer 3
A is correct. A is 31 + 28 + 31 + 9. B includes April 10. C counts only January through March. D adds two days to the correct seller period.
Change the fact: the actual-calendar year is a leap year with the same dates. February contributes 29, so the seller count is 100. Choose the year denominator from the stated method separately.
4. The seller collected the buyer's rental income
The seller received tenant rent before closing. An agreed $900 portion belongs to the buyer's post-closing period. Which simplified entry transfers that portion?
- Seller credit and buyer debit
- No entry because every prepaid item belongs to the seller
- Seller debit and buyer credit
- Debit both parties $900
Show answer 4
C is correct. A reverses who holds the buyer's income. B ignores the agreed allocation. C transfers the $900 through matching entries. D does not balance the transfer.
Change the fact: the seller instead paid a transferable expense for the buyer's period, and the problem requires reimbursement. That different fact gives a seller credit and buyer debit.
5. Keep the daily rate's precision
Annual tax is $8,765. Use 365 as the denominator and 200 supplied responsible days. Round only the final answer to cents. What is the share?
- $4,802.00
- $24.01
- $8,765.00
- $4,802.74
Show answer 5
D is correct. A rounds the daily rate too early. B is only a rounded daily rate. C is the full annual amount. D rounds $8,765 × 200 ÷ 365 at the end.
Change the fact: a different exercise expressly requires daily-rate rounding first. Follow that exercise and identify the rounding instruction when comparing results.
6. The leap-year basis is supplied
An exercise states an actual-year 366-day basis, a $7,320 annual amount and 60 responsible days. What is the share?
- $1,200
- $1,203.29
- $1,220
- $7,320
Show answer 6
A is correct. A uses $7,320 ÷ 366 × 60. B substitutes 365. C substitutes 360. D ignores the partial period.
Change the fact: the instruction expressly fixes the basis at 365. With the same supplied 60 days, the rounded share is $1,203.29. A leap year does not authorize silently overriding that instruction.
Proration questions answered
Which proration method should I use on the Illinois broker exam?
Use the complete instructions in the question, including its denominator, day-count rule and closing-day allocation. The June 24, 2026 PSI outline names prorations; that topic heading does not establish a universal 360-day default. If a study question omits a necessary assumption, identify it instead of claiming that this page supplies the missing official exam rule.
Does a leap year always require a 366-day denominator?
No. Use 366 when the stated actual-year convention calls for it. A fixed Actual/365 instruction still specifies 365, and a 30/360 instruction still specifies 360. Within an actual-year example, February 29 changes the calendar count. For a period crossing years or a specialized loan method, use its complete instructions rather than extending a single-year classroom shortcut.
What should I do with the 31st or the end of February under 30/360?
Follow the specific convention supplied. Month-end adjustments differ among 30/360 methods. The examples here deliberately give simple dates or a day count and do not prescribe one universal February or 31st-day adjustment. Assign closing day to one party under the stated rule; month-end adjustments are a separate question.
Check your method before checking your score
The June 24, 2026 PSI outline, national XI.A.3, names real property tax and other prorations. The whole Real Estate Calculations area is 7% of the 100 scored national broker questions, not seven proration questions. State II.J.4 also names prorations within the wider Illinois License Act area.
Use the math drill for further calculation practice. To keep practicing for the broker exam between study sessions, you can download Pass Illinois. Explain the day count and payment direction as well as the answer.