Earned Premium Across Accounting Periods

Introduction

A policy may begin in one accounting period and end in another. The insurer records written premium for the policy, but that amount is not all earned at once: premium is earned as the insurer provides coverage. To report results for a particular period, the premium must be allocated to the coverage provided during that period.

For a simple policy with a fixed premium, a common allocation is proportional to covered days. This tutorial develops that method, shows how to apply it across year-end, and explains when a straight-line day allocation may not represent the underlying risk. The method is aligned with the CAS Exam 5 (Basic Ratemaking and Estimated Claim Liabilities) syllabus.

Definition: Written premium is the premium recorded as written for a policy. Earned premium is the portion allocated to coverage already provided during a specified period. Unearned premium is the portion of written premium attributable to coverage not yet provided as of a specified date. For a single policy, absent adjustments, written premium equals the sum of earned and unearned premium over the relevant coverage and remaining term.

Day-Based Allocation

For a simple policy, let $P$ be its written premium, let $D$ be the total number of covered days in its term, and let $d_j$ be the number of those covered days that fall in accounting period $j$. Under a straight-line, day-pro-rata allocation, the premium earned in period $j$ is:

EP_j = P \frac{d_j}{D}.

The policy term’s beginning and ending dates determine which days are covered. In the examples below, the inception date and the stated expiration date are both included as covered dates. Equivalently, count the days from inception up to, but not including, the day after expiration. This convention avoids accidentally omitting the final covered day.

The method assumes that premium is earned evenly per covered day. It is appropriate for a simple pro-rata allocation when no different earning pattern is specified. It does not model seasonal exposure, changing risk over the term, or an endorsement that changes the premium or coverage. Those circumstances may require a different allocation or adjustment. Do not confuse the date premium is collected or recorded with the dates on which coverage is provided.

Why the Formula Works

The day-pro-rata method assigns the same fraction of total premium to each covered day. With $D$ covered days, the amount assigned to one day is $P/D$. If $d_j$ covered days fall in a period, adding the amount for those days gives:

EP_j = d_j\frac{P}{D} = P\frac{d_j}{D}.

If the accounting periods partition the entire policy term, their day counts satisfy $\sum_j d_j = D$. Therefore:

\sum_j EP_j = \sum_j P\frac{d_j}{D} = \frac{P}{D}\sum_j d_j = P.

This reconciliation is an important check: if all covered days have been allocated exactly once, period-earned premium sums to written premium. At a date partway through the term, the same reasoning gives unearned premium as written premium multiplied by the fraction of covered days remaining.

Worked Example: A Policy Crossing Year-End

A hypothetical policy covers November 1, 2026 through October 31, 2027, inclusive, and has written premium of $2,400. Using exact calendar days and straight-line earning, calculate premium earned in calendar year 2026 and unearned premium at December 31, 2026.

Method. Count the total covered days and the covered days through December 31. The 2026 portion is November 1 through December 31: November has 30 days and December has 31, for $30+31=61$ days. The full policy term has 365 days: 61 days in 2026 and 304 days from January 1 through October 31, 2027.

Earned in 2026. Apply the day-pro-rata formula:

EP_{2026} = \$2{,}400\frac{61}{365} = \$401.095890\ldots = \$401.10.

The result is rounded to the nearest cent. The 2026-earned amount is $401.10.

Unearned at December 31, 2026. There are 304 covered days remaining:

UP_{12/31/2026} = \$2{,}400\frac{304}{365} = \$1{,}998.904109\ldots = \$1{,}998.90.

Check. The unrounded amounts sum to $2,400 because $61+304=365$. The rounded amounts also reconcile: $\$401.10+\$1{,}998.90=\$2{,}400.00$. The answer is not $400 earned and $2,000 unearned: those figures may look like a convenient split, but they do not follow from the exact-day allocation.

Splitting Premium Across Periods

For a policy spanning more than one accounting period, calculate each period’s covered days separately. Use the number of covered days in that period, not the number of days in the calendar year as the denominator. The denominator is the total covered days in the policy term.

Identify the policy term.
Record the inclusive coverage start and expiration dates, then count all covered days to find $D$.

Divide the term at accounting-period boundaries.
Count the covered days falling in each period. Check that the period counts add to $D$.

Allocate the premium.
For each period, multiply written premium by that period’s day count divided by $D$.

Reconcile.
Check that the allocated amounts sum to written premium, allowing only for any cent-level rounding.

Worked Example: Two Calendar Years with Different Day Counts

A hypothetical policy covers July 1, 2025 through June 30, 2026, inclusive, for a written premium of $1,825. Find the premium earned in each calendar year using exact covered days.

Method. The term has 365 days. July through December 2025 contain $31+31+30+31+30+31=184$ covered days. January through June 2026 contain $31+28+31+30+31+30=181$ covered days. The check is $184+181=365$.

The daily premium under this allocation is $\$1{,}825/365=\$5$. Therefore:

EP_{2025} = \$1{,}825\frac{184}{365} =184(\$5)=\$920, $$ $$ EP_{2026} = \$1{,}825\frac{181}{365} =181(\$5)=\$905.

Check. The allocated amounts sum to the written premium: $\$920+\$905=\$1{,}825$. A 50/50 split would be incorrect because the policy provides 184 covered days in 2025 and 181 in 2026.

Worked Example: A Term That Includes February 29

A hypothetical policy covers December 1, 2027 through November 30, 2028, inclusive, and has written premium of $3,660. Calculate the premium earned in calendar years 2027 and 2028. Use straight-line earning by covered day.

Method. The policy term contains 366 days because it includes February 29, 2028. December 1 through December 31, 2027 contributes 31 covered days. January 1 through November 30, 2028 contributes $31+29+31+30+31+30+31+31+30+31+30=335$ covered days. Together, $31+335=366$.

The premium per covered day is $\$3{,}660/366=\$10$. Thus:

EP_{2027} = 31(\$10)=\$310, \qquad EP_{2028} = 335(\$10)=\$3{,}350.

Check. The allocation sums to $\$310+\$3{,}350=\$3{,}660$. Using 365 as the denominator would ignore a covered day and would fail to allocate the correct premium across the term. Count the actual covered days; do not assume every policy term has 365 days.

Common Mistakes and Practical Checks

A reliable calculation keeps three quantities distinct: total written premium, total covered days in the policy term, and covered days in the accounting period being measured. Confusing any of them can distort the allocation.

Common mistake	Why it fails	Correction
Using the number of days in the calendar year as the denominator	The denominator must represent the policy’s full covered term, which may be shorter, longer, or cross a leap day.	Count the policy-term days first, then count each period’s share.
Counting one endpoint but omitting the other	An inclusive expiration date is a covered day under the convention used here.	Include both stated coverage endpoints and verify the total term length.
Dividing premium equally between years	Calendar years may contain different numbers of the policy’s covered days.	Allocate in proportion to each year’s covered-day count.
Rounding intermediate values	Repeated rounding can make the period allocations fail to reconcile.	Retain full precision during the calculation and round money only at the end.

For an ending unearned amount on a single, unchanged policy, calculate the premium attributable to the remaining covered days, or subtract cumulative earned premium from written premium. Both approaches should agree before rounding. If they do not, recheck the date boundaries and day counts.

Key takeaway: Under straight-line day-pro-rata earning, a period receives the fraction of written premium equal to its share of the policy’s covered days. Use exact dates, count the actual term days, and reconcile all period allocations to written premium.

Check Your Understanding

For each hypothetical policy, use inclusive coverage dates and straight-line earning. Round dollar answers to the nearest cent where needed.

A policy covers April 1 through September 30, 2026, inclusive, for $1,830. How many days fall in April through June and in July through September, and how much premium is earned in each of those two periods? (Answer: 91 days and $910 in April–June; 92 days and $920 in July–September.)
A policy covers January 1 through December 31, 2028, inclusive, for $3,660. How many days fall in January through June and in July through December, and what premium is earned in each half-year? (Answer: 182 days and $1,820 in January–June; 184 days and $1,840 in July–December.)
A policy covers August 15, 2025 through August 14, 2026, inclusive, for $7,300. Calculate 2025 earned premium and unearned premium at December 31, 2025. (Answer: 139 of 365 days are in 2025; earned premium is $2,780 and unearned premium is $4,520.)
A policy covers October 1, 2027 through March 31, 2028, inclusive, for $3,660. Allocate premium between calendar years. (Answer: 92 of 183 days fall in 2027, earning $1,840; 91 of 183 days fall in 2028, earning $1,820.)
A policy covers July 1, 2026 through June 30, 2027, inclusive, for $3,650. Calculate 2026 earned premium and unearned premium at December 31, 2026. (Answer: 184 of 365 days fall in 2026; earned premium is $1,840 and unearned premium is $1,810.)

What You'll Learn