Why Timing Errors Change the Result
Insurance transactions have several relevant dates, and those dates answer different questions. A policy may be issued in one accounting period while its coverage extends into another. A claim may arise from an event in one year, be reported later, and be paid later still. Treating these dates as interchangeable can misstate premium, claim cost, or the period to which experience belongs.
This tutorial focuses on three distinctions: written premium versus earned premium, cash paid versus incurred claim cost, and accounting-year results versus accident-year results. The calculations below assume ordinary accrual accounting, straight-line premium earning when coverage is uniform over time, and claim amounts measured on a consistent undiscounted basis. If coverage is not uniform over time, the appropriate earning pattern may differ from straight-line.
Written Premium Is Not Automatically Earned
The date premium is written identifies when the insurer records the policy transaction; it does not establish that all the contracted coverage has already been provided. Under straight-line earning, premium is earned in proportion to the elapsed coverage time. This is an assumption about how risk is provided over the policy term, not a universal rule for every insurance product.
For a policy with uniform coverage and no midterm change, the portion of its premium earned in an accounting period is the policy premium multiplied by the fraction of the policy term that overlaps that period. The policy term and the accounting period must be compared by dates, rather than by the year in which the premium was written.
The formula follows by dividing the total premium into equal earning amounts per unit of coverage time. If a policy has premium \(P\) for \(T\) equal time units, the assumed earning per unit is \(P/T\). If \(k\) of those units fall in the accounting period, that period earns \(k(P/T)\), or \(P(k/T)\). The result is valid under the stated straight-line assumption; it may not fit coverage whose risk or premium earning pattern varies materially over time.
Worked Example: A Policy Written Before Most Coverage Is Provided
A hypothetical insurer writes a policy on October 1, 2025, for a premium of $1,460. Coverage runs from October 1, 2025, through September 30, 2026. Assume uniform coverage and straight-line earning. Find the premium earned in calendar year 2025 and the unearned premium at December 31, 2025.
Step 1: Identify the full coverage term. The policy covers 12 months, from October 2025 through September 2026. The premium per month under the straight-line assumption is $1,460 ÷ 12 = $121.6667.
Step 2: Count the months of coverage provided in 2025. The calendar year includes October, November, and December of this policy term: 3 months.
Step 3: Calculate 2025 earned premium. The calculation before rounding is $1,460 × 3 ÷ 12 = $365.
Step 4: Calculate the amount not yet earned at year-end. Nine months of coverage remain, so the unearned amount is $1,460 × 9 ÷ 12 = $1,095. Check: $365 + $1,095 = $1,460, the full policy premium.
Method and trap avoided. This is pro rata earning by coverage time. Recording all $1,460 as 2025 earned premium merely because the policy was written in 2025 would overstate earned premium by $1,095.
Paid Claims and Incurred Claims Measure Different Things
A payment date tells when cash left the insurer. It does not, by itself, tell when the claim cost belongs in an incurred result. A claim from an earlier period can be paid now, while a claim arising now can remain unpaid. For a calendar accounting period, paid claims are therefore reconciled to incurred claims by accounting for the change in unpaid claim liabilities.
The relationship follows from a simple roll-forward. The period begins with a liability for previously recognized but unpaid costs. During the period, payments reduce that liability or settle newly recognized claims. At period-end, the remaining unpaid amount is still owed or estimated to be owed. Thus the claims recognized during the period must equal the cash paid, plus the amount still unpaid, minus the amount that was already carried into the period. The formula is a reconciliation, not a method for predicting ultimate claims.
Worked Example: A Payment Is Not the Same as the Period’s Claim Cost
A hypothetical insurer begins 2025 with an unpaid claim liability of $30,000. It pays $60,000 in claims during 2025 and ends the year with an unpaid claim liability of $45,000. Calculate 2025 incurred claims and compare them with paid claims.
Step 1: Record the inputs on the same basis. Beginning unpaid liability = $30,000; 2025 paid claims = $60,000; ending unpaid liability = $45,000.
Step 2: Reconcile payments and the liability change. The liability increased by $45,000 − $30,000 = $15,000. Therefore, incurred claims are $60,000 + $15,000 = $75,000.
Step 3: Check the interpretation. Incurred claims exceed paid claims by $15,000, exactly the increase in unpaid liability. If the liability had decreased instead, incurred claims would be below paid claims, all else equal.
Method and trap avoided. This is the paid-plus-change-in-liability reconciliation. Calling the $60,000 cash payment the full 2025 incurred amount would understate incurred claims by $15,000.
The reconciliation requires consistent definitions. For example, do not combine paid losses excluding an expense category with liabilities that include that category. Also ensure that beginning and ending liabilities use compatible valuation dates and measurement bases. The arithmetic is simple; inconsistent inputs make its result misleading.
Calendar-Year and Accident-Year Results Use Different Date Rules
A calendar year is a fixed accounting interval, such as January 1 through December 31. Calendar-year paid claims are assigned according to payment dates. Calendar-year incurred claims are measured for that accounting interval using the applicable incurred-cost accounting and liability movement.
An accident year groups claims by the year in which the insured event occurred. A claim can belong to one accident year even if it is reported or paid in a later calendar year. When discussing an accident-year result, be precise about whether the measure is paid to date, incurred to date, or estimated at another development point: the accident-year label identifies the occurrence cohort, but does not by itself specify the valuation measure.
| Measure | Date rule for assigning a transaction or claim | Question it answers |
|---|---|---|
| Calendar-year paid claims | Date the payment is made | How much claim cash was paid in this calendar year? |
| Calendar-year incurred claims | Accounting period, including the change in unpaid liability | What claim cost was recognized for this calendar year? |
| Accident-year incurred claims | Year of the insured event, measured on a stated basis | What claim cost is attributed to events in this accident year? |
Worked Example: The Same Claims Under Calendar-Year and Accident-Year Views
A hypothetical insurer has the following claim information. Amounts are in dollars. The January 1, 2025, unpaid liability is $22,000, consisting of $12,000 for claim A and $10,000 for claim D. During 2025, claim A, from a 2024 accident, is paid $12,000; claim D, also from a 2024 accident, is paid $7,000; claim E, from a 2025 accident, is incurred and paid at $6,000; claim B, from a 2025 accident, is incurred at $30,000 and remains unpaid; and claim C, from a 2025 accident, is incurred at $8,000, of which $3,000 is paid. At December 31, claim D’s remaining liability is $5,000, claim B’s is $30,000, and claim C’s is $5,000. Assume no other claims or liability changes.
Step 1: Calculate calendar-year paid claims. Payments made during 2025 are $12,000 + $7,000 + $6,000 + $3,000 = $28,000. This total includes payments on two claims from 2024.
Step 2: Calculate the ending unpaid liability. The listed year-end amounts total $5,000 + $30,000 + $5,000 = $40,000. The beginning liability is $22,000.
Step 3: Calculate calendar-year incurred claims. Using the liability reconciliation, $28,000 + $40,000 − $22,000 = $46,000. The increase in liability is $18,000, so incurred claims exceed calendar-year payments by that amount.
Step 4: Calculate accident-year 2025 incurred claims. Include claims from 2025 accidents: E at $6,000, B at $30,000, and C at $8,000. Their total is $6,000 + $30,000 + $8,000 = $44,000. Do not include claims A and D, which arose from 2024 accidents.
Step 5: Reconcile the difference in viewpoint. Calendar-year incurred claims are $46,000, while accident-year 2025 incurred claims are $44,000. The $2,000 difference is the increase in claim D’s liability from its $10,000 opening amount to its $12,000 total cost recognized by year-end ($7,000 paid + $5,000 unpaid). This is development on a prior accident year. The check is $44,000 for 2025 accidents plus $2,000 for the prior-year change = $46,000 calendar-year incurred.
Method and trap avoided. The calendar-year result uses payments and liability movement; the accident-year result groups costs by occurrence date. A common error is to assign every payment made in 2025 to accident year 2025, which would incorrectly include $19,000 paid on claims A and D.
A Reliable Date-Based Check
When a period result appears unexpectedly high or low, first label the date attached to each item. For premium, identify the policy transaction date and the coverage dates. For claims, distinguish occurrence, reporting, and payment dates, then identify whether the requested result is paid, incurred, calendar-year, or accident-year. Only after those labels are clear should the amounts be added or reconciled.
Determine whether the question asks for written premium, earned premium, paid claims, incurred claims, or an accident-year result.
Use coverage dates for earning premium, payment dates for paid claims, and occurrence dates for accident-year grouping.
Use a coverage-time allocation for earned premium under a stated earning assumption, or reconcile claims through the change in unpaid liabilities.
Confirm that premium earned and unearned reconcile to the policy premium, or that paid claims plus the liability change reconcile to incurred claims.
The most common exam trap is to notice a familiar number and use it without checking its date. Written premium may be mistaken for earned premium because both are recorded amounts; claim payments may be mistaken for incurred claims because both concern claims; and a payment year may be mistaken for an accident year. These shortcuts answer different questions from the ones asked.
Check Your Understanding
For each problem, identify the relevant date basis before calculating.
- A hypothetical annual policy has a $2,400 premium and provides uniform coverage from July 1, 2026, through June 30, 2027. Under straight-line earning, how much is earned in calendar year 2026 and how much remains unearned at December 31, 2026? (Answer: $1,200 earned; $1,200 unearned.)
- An insurer has beginning unpaid claims of $17,000, pays $48,000 during the year, and has ending unpaid claims of $23,000. What are incurred claims for the year? (Answer: $54,000.)
- A $900 policy is written on April 1 for coverage from April 1 through September 30, with uniform coverage. Under straight-line earning, how much is earned by June 30? (Answer: $450.)
- During 2027, an insurer pays $9,000 on a claim from an event in 2026 and $4,000 on a claim from an event in 2027. What amount is assigned to calendar-year 2027 paid claims, and how much of those payments belongs to accident year 2027? (Answer: $13,000 of calendar-year paid claims; $4,000 is from accident year 2027.)
- Beginning unpaid liability is $40,000, calendar-year payments are $75,000, and ending unpaid liability is $32,000. Of the incurred claims, $50,000 is attributed to accidents in the current year. What are total calendar-year incurred claims and the amount of incurred claims attributable to prior-year development? (Answer: $67,000 total calendar-year incurred; $17,000 prior-year development, since $67,000 − $50,000 = $17,000.)