A Worked Accrual Example for a Policy Crossing Year-End

Why a Policy Crossing Year-End Needs Several Views

A policy can be issued, billed, collected, and earned on different dates. Those dates answer different accounting questions. A bill creates or confirms an amount due; a collection changes cash and the receivable; coverage over time determines how much premium is earned. When the policy crosses a reporting date, recording the full annual premium as that year’s revenue merely because it was billed or collected can misstate the period’s results.

This worked accrual example follows premium and a directly attributable acquisition cost across two calendar years. It focuses on the timing of those amounts, not claim recognition. The numerical examples use a simplified accounting presentation and explicit assumptions; actual recognition and deferral rules depend on the applicable accounting framework and the facts of the contract.

Definition: Written premium is premium recorded when a policy is written under the stated accounting convention. Earned premium is the portion attributable to coverage already provided. Unearned premium is the portion attributable to future coverage and is shown here as a liability. Cash collected is the amount received from the policyholder, while a premium receivable is an amount billed or otherwise due but not yet collected.

Allocation Assumptions and Reconciliation

For the examples, assume a fixed-premium policy with no endorsements, cancellations, audits, or changes in coverage. Coverage is provided uniformly by day, so premium is earned in proportion to covered days. Use actual calendar days in the policy term, with the effective date included and the expiration date excluded. This makes a term from October 1 through the start of the following October 1 a 365-day term when it contains no February 29.

For a policy with total premium $P$, term length $N$ days, and $n$ covered days in an accounting period, the day-based allocation is:

\text{Premium earned in the period}=P\frac{n}{N}

If the policy’s premium has been written in full, the period-end unearned premium is the portion for the remaining coverage days. With no opening unearned premium or other adjustments, the relationship for the period is:

\text{Earned premium} = \text{Written premium} - \text{Increase in unearned premium}

This relationship explains why billing and collection do not determine earned premium. They affect receivables and cash, while the coverage period determines the allocation between earned premium and unearned premium.

Assumption for acquisition expense: In these examples, a directly attributable acquisition cost is eligible for deferral and is recognized as expense in the same proportion as the related premium is earned. The unrecognized portion is shown as a deferred acquisition cost (DAC) asset. This is an explicit modeling assumption, not a claim that every accounting framework permits the same deferral.

The allocation follows from the uniform-coverage assumption. If each of $N$ days provides the same amount of coverage, each day accounts for $1/N$ of the total premium. After $n$ days, $n$ equal daily portions have been earned, giving $P(n/N)$. The remaining $(N-n)$ portions relate to future coverage, so unearned premium is $P((N-n)/N)$. Adding the earned and unearned portions gives the original premium:

P\frac{n}{N}+P\frac{N-n}{N}=P

This allocation is not appropriate without qualification when coverage is materially seasonal, premium varies with exposure, or a contract is adjusted by an audit or endorsement. In those cases, the earning pattern or premium amount may not be uniform by day.

Worked Accrual Example

Worked Example: An Autumn Policy With Installment Collections

A hypothetical commercial package policy is issued on September 15, 2025, for coverage from October 1, 2025, through September 30, 2026. The annual premium is $1,460, billed in full at issue. The insurer collects $900 on October 5, 2025, and the remaining $560 on January 10, 2026. A directly attributable acquisition commission of 15% of premium is paid at issue and, under the stated assumption, deferred and expensed in proportion to premium earned. Calculate the premium, cash, receivable, and acquisition-expense amounts for 2025 and 2026, including the December 31, 2025 balances.

Method. Allocate premium and commission by covered days; track collection and receivable separately. The term has 365 days. October through December 2025 has $31+30+31=92$ covered days, leaving $365-92=273$ days in 2026.

Written premium and cash. Under the stated convention, the full $1,460 is written when the policy is issued in 2025. The invoice creates a $1,460 receivable. The October collection reduces that receivable by $900, leaving $560 at December 31. The 2025 cash collected is $900; the remaining $560 is collected in 2026. Collection timing does not change the amount of premium earned.

Earned and unearned premium. The daily premium is $1460/365=\$4$. Therefore, 2025 earned premium is $92\times \$4=\$368$. The December 31 unearned premium is $273\times \$4=\$1,092$. These amounts reconcile to the written premium: $\$368+\$1,092=\$1,460$. In 2026, the remaining 273 days earn $1,092, leaving no unearned premium at expiration.

Acquisition cost. The total commission is $0.15\times \$1,460=\$219$. The 2025 expense is $92/365\times \$219=\$55.20$, because the commission rate is 15% of the $368 earned premium. The remaining $163.80 is deferred at December 31. In 2026, that $163.80 is expensed as the remaining premium is earned. Total expense over the term is $219.

Check. Across both years, earned premium totals $\$368+\$1,092=\$1,460$, and commission expense totals $\$55.20+\$163.80=\$219$. At December 31, the $560 receivable is not the same balance as the $1,092 unearned premium: one measures unpaid billed premium, the other measures premium for future coverage.

Record the written amount.
When the premium is written and billed, record the premium and the amount due. A collection later reduces the receivable and increases cash; it does not itself earn premium.

Count covered days in the period.
Apply the stated day-count convention to the policy term and split the coverage days at the accounting date.

Allocate premium and eligible acquisition cost.
Use the same earned proportion under the uniform-coverage and deferral assumptions. Reconcile earned and unearned amounts to the written premium and total acquisition cost.

Keep ending balances distinct.
Report cash, receivable, unearned premium, and any deferred acquisition cost separately. They represent different rights, obligations, or timing differences.

Two Further Worked Examples

Worked Example: A Spring Policy Paid in Two Installments

A hypothetical equipment policy provides coverage from March 1, 2025, through February 28, 2026. Its 365-day term premium is $1,825. The full premium is billed at inception. The policyholder pays $1,000 on March 1, 2025, and $825 on October 1, 2025. A directly attributable acquisition cost is 10% of premium, paid at inception and deferred in proportion to premium earned. Find the earned premium and acquisition expense by calendar year, the December 31, 2025 unearned premium and DAC, and the year-end receivable.

Method. Count the days in each calendar year. March through December 2025 contains $31+30+31+30+31+31+30+31+30+31=306$ days. January and February 2026 contain $31+28=59$ days. The two counts sum to the stated 365-day term.

The daily premium is $1825/365=\$5$. Thus 2025 earns $306\times \$5=\$1,530$, and 2026 earns $59\times \$5=\$295$. The unearned premium at December 31, 2025, is $\$1,825-\$1,530=\$295$, corresponding to the 59 remaining days.

The total acquisition cost is $10\%\times \$1,825=\$182.50$. Its 2025 expense is $10\%\times \$1,530=\$153.00$, leaving DAC of $\$182.50-\$153.00=\$29.50$ at year-end. The 2026 expense is $29.50. Both installments have been collected by October 1, so the December 31 premium receivable is $0. The year-end unearned premium is $295, not the receivable: the former relates to future coverage, and the latter is an unpaid amount due.

Check. Earned premium is $\$1,530+\$295=\$1,825$; acquisition expense is $\$153+\$29.50=\$182.50$. The day counts and both financial totals reconcile.

Worked Example: A December Policy With an Unpaid Installment

A hypothetical liability policy covers December 1, 2024, through November 30, 2025, a 365-day term. Premium of $730 is billed on December 1, 2024. The insurer collects $400 that day and $330 on March 1, 2025. A 20% directly attributable acquisition cost is paid at inception and deferred in proportion to earned premium. Calculate earned premium and acquisition expense for each calendar year, plus unearned premium, DAC, and premium receivable at December 31, 2024.

Method. December 2024 has 31 covered days. The remaining 2025 coverage has $365-31=334$ days. The daily premium is $730/365=\$2$. Therefore, 2024 earns $31\times \$2=\$62$; 2025 earns $334\times \$2=\$668$. Unearned premium at December 31, 2024, is $334\times \$2=\$668$.

The total acquisition cost is $20\%\times \$730=\$146$. The 2024 expense is $20\%\times \$62=\$12.40$, leaving $\$146-\$12.40=\$133.60$ as DAC. The 2025 expense is $133.60. The $400 collection leaves a premium receivable of $\$730-\$400=\$330$ at December 31, 2024; that balance is collected in March 2025.

Check. The premium allocations reconcile: $\$62+\$668=\$730$. The expense allocation also reconciles: $\$12.40+\$133.60=\$146$. At the end of 2024, unearned premium is $668, DAC is $133.60, and the receivable is $330; none of these balances should be substituted for another.

Common Timing Trap

A frequent error is to treat the amount collected during the year as earned premium. In the first example, that mistaken calculation would report 2025 earned premium as $900, the cash collected, and 2025 acquisition expense as $15\%\times \$900=\$135$. Both figures are wrong under the stated coverage-day method: only 92 of 365 coverage days have elapsed by December 31.

The correction is to calculate earned premium from coverage: $1460\times 92/365=\$368$. The corresponding acquisition expense is $219\times 92/365=\$55.20$. Separately, report $900 cash collected and a $560 receivable. This distinction is aligned with the CAS Exam 5 (Basic Ratemaking and Estimated Claim Liabilities) syllabus.

A second trap is to record all eligible acquisition cost as current expense simply because it was paid at issue. Under the deferral assumption used here, payment establishes the cash outflow and DAC asset; the portion matched to coverage already provided is the expense. Do not apply that treatment automatically: first confirm the applicable accounting basis and whether deferral is permitted.

Key takeaway: For a policy crossing year-end, calculate earned premium from the coverage provided, then track cash collections, receivables, unearned premium, and acquisition costs on their own bases. Reconcile each total over the full policy term.

Check Your Understanding

For each hypothetical policy, use uniform coverage by day and the stated deferrable-acquisition-cost assumption where applicable. Answers use the effective-date-included, expiration-date-excluded convention.

A policy covers July 1, 2025, through June 30, 2026, and has premium of $1,095. It is billed and collected in full on July 1. How much premium is earned in 2025, and what is unearned premium at December 31, 2025? (Answer: 2025 earned premium $552; unearned premium $543.)
A policy covers November 1, 2025, through October 31, 2026, for $2,190. The full premium is collected at inception. Calculate 2025 earned premium and the December 31 unearned premium. (Answer: 2025 earned premium $366; unearned premium $1,824.)
A $1,460 policy covers October 1, 2025, through September 30, 2026. It has a 12% acquisition cost that is paid and deferred at issue. Find 2025 earned premium, 2025 acquisition expense, and December 31 DAC. (Answer: earned premium $368; acquisition expense $44.16; DAC $131.04.)
A policy covers April 1, 2025, through March 31, 2026, with premium of $2,190 and a 8% deferrable acquisition cost. Find the earned premium and acquisition expense for each calendar year. (Answer: 2025 earned premium $1,650 and expense $132; 2026 earned premium $540 and expense $43.20.)
A policy is issued, billed, and fully collected on December 20, 2025, for coverage from January 1 through December 31, 2026. Premium is $1,460, and a 10% directly attributable acquisition cost is paid at issue and deferred. Under the stated convention, what are 2025 earned premium, December 31, 2025 unearned premium, December 31 DAC, and 2026 acquisition expense? (Answer: 2025 earned premium $0; unearned premium $1,460; DAC $146; 2026 acquisition expense $146.)

What You'll Learn