Math Walkthrough
Proration Walkthrough: Day Counts and Entries
Day-count conventions, billing cycles, and the treatment of the closing day are set by jurisdiction, by contract, or by the exam item itself. No figure below describes any particular place. Exam questions supply their own conventions, and for an actual transaction the settlement agent applies local practice.
Prorating means splitting a charge that covers a stretch of time between two owners who each held the property for part of it. Taxes, association dues, ground rent and prepaid service contracts all get handled this way at settlement.
What follows is one worked path from the stem to the settlement entry, taken slowly, with the two places candidates lose points marked as they come up: the day count at the boundary, and the choice of which party gets debited.
Pick the Denominator First
Before any arithmetic, settle on how long the period is in the units you intend to use. Two conventions are in circulation and they produce different daily rates from the same annual figure.
A statutory or banker's year treats every month as thirty days, giving a 360-day year. It makes mental arithmetic easy and the numbers come out round, which is why older material and some exam items still use it. A calendar year counts actual days, so the daily rate reflects a 365-day year and February and July are no longer interchangeable.
The difference is real but small: the same annual amount produces a daily rate roughly one and a half percent higher under the shorter year. That gap is enough to move your result away from the intended choice and onto one of the distractors, which is the only reason it matters for scoring purposes.
Some charges are not annual at all. Association dues arrive monthly or quarterly and ground rent may run on its own cycle. Divide by the period actually covered by the amount you were given, not by a year out of habit.
The Walkthrough, Step by Step
Work in this order every time. The sequence is what keeps a correct figure from landing on the wrong line.
Read the charge and its span. Write down the dollar amount and the exact window it covers. If the stem says quarterly, your denominator is a quarter.
Choose the day-count convention the item specifies, or the one the transaction uses. Thirty-day months mean a 360-day year; actual dates mean 365.
Divide to get the unit rate. Carry the full decimal forward rather than rounding here, and round only once at the end.
Settle the closing day. Decide whether it belongs to the seller or the buyer, and write that decision down before counting, not during.
Count the seller's units from the start of the period to the boundary you just set. Count months first where you can, then add the remaining days, which is faster and less error-prone than counting days across the whole span.
Multiply the unit rate by the seller's count. The remainder of the period is the buyer's, and the two pieces must add back to the original total.
Decide the direction from the billing cycle, then post the paired entry: one party debited, the other credited, same amount.
Three Full Walkthroughs
Original items written for this page, not drawn from any licensing examination. Each solution shows every step rather than just the result.
Question 1
An item gives an annual charge of $4,380, billed after the period it covers, a closing on the sixtieth day of the calendar year, a 365-day convention, and the seller holding the day of closing. Produce the settlement entry.
Step one, the charge is $4,380 for a full calendar year. Step two, the convention is 365 actual days. Step three, the daily rate is 4,380 divided by 365, which is $12 exactly. Step four, the seller owns the closing day, so the boundary falls at the end of day sixty. Step five, the seller's count is 60 days. Step six, 60 times 12 gives $720 for the seller, leaving 305 days worth $3,660 for the buyer, and the two sum to $4,380. Step seven, the bill comes after the period, so the buyer will pay all of it and the seller owes its share now: debit the seller $720, credit the buyer $720.
Question 2
An association in the item charges $900 per quarter, collected at the start of the quarter. Closing occurs one month and fifteen days into the quarter, using thirty-day months. Produce the entry.
The span is one quarter and the amount covering it is $900. Under thirty-day months a quarter is 90 days, so the daily rate is 900 divided by 90, or $10. The seller held one month plus fifteen days, which is 30 plus 15, or 45 days, worth $450. The buyer's remaining 45 days are also worth $450. The money was collected at the start of the quarter, so the seller has paid for 45 days it will not occupy: credit the seller $450 and debit the buyer $450.
Question 3
An item gives an annual charge of $2,920 billed behind, a closing at the end of the fourth month, a 360-day convention, and asks for the buyer's credit.
Divide by 360 rather than 365 because the item said so: 2,920 divided by 360 is about $8.1111 per day, which is worth keeping unrounded. Four full months under this convention is 120 days. The seller's share is 120 times 8.1111, which comes to $973.33 after rounding at the end. Billed behind means the seller owes that amount, so the buyer's credit is $973.33 and the seller's debit matches it. Had you rounded the daily rate to $8.11 first, you would be off by a few cents, which is enough to miss an intended answer choice.
The Boundary Day and the Off-by-One
Most wrong answers on this topic are one unit away from the right one, and the cause is almost always the closing day. Whether that day belongs to the seller or the buyer is a convention, not a calculation, and the two treatments produce answers separated by exactly one daily rate.
Exam items normally state it outright, with language about the seller being responsible through closing or the buyer being responsible from the day of closing. When that sentence is present, it is doing work; read it before you start counting.
Counting itself is also a place to be deliberate. Adding up whole months and then the leftover days is faster than walking a calendar, and it fails less often. Under a thirty-day convention every month contributes thirty regardless of the calendar, which is the entire appeal of that method.
Before you commit, run a proportion check. If the closing sits about a third of the way through the period, the seller's share should sit near a third of the total. This will not catch a one-day error, but it catches every decimal slip, every inverted division and every reversed subtraction, which are the errors that produce badly wrong answers rather than slightly wrong ones.
Walkthrough Questions
How do I tell which convention an item wants?
Look for an explicit instruction first; most items include one. Failing that, a reference to thirty-day months or a banker's year means 360, and exact calendar dates with no such reference generally mean actual days. For a real transaction the settlement agent follows local practice rather than either default.
Which party is debited when the bill has not yet been issued?
The seller. If the charge is billed after the period it covers, the buyer will receive and pay the entire bill even though the seller occupied part of the period. The seller's portion is therefore taken from the seller at settlement and handed to the buyer, which is a debit to the seller and a credit to the buyer.
What exactly do debit and credit mean on a settlement statement?
A debit is a charge against a party that reduces what that party takes away or increases what it must bring. A credit runs the other direction. A proration always appears twice, once as each, because the amount is being moved between the two parties rather than paid to an outsider.
When should I round?
Once, at the end. Rounding the daily rate before multiplying compounds the error across every unit in the count, and an answer a few cents off is treated as wrong. Carry the decimals through the multiplication and round the final dollar figure.
Do the buyer's and seller's shares always add up to the whole amount?
For a single period, yes, and that is your best structural check. If they do not, either the count is wrong or you divided by a period different from the one the amount covers. Charges spanning more than one billing period should be handled one period at a time.
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