Integrated Insurance Accounting Period Exercise

Why an Integrated Period Analysis Matters

An insurance transaction can have more than one relevant date. A premium may be collected when coverage begins but earned over the coverage period. A claim may be paid in a different accounting period from the one in which the loss occurred. An expense may be paid in advance or after the service has been received. To interpret a period’s results correctly, keep the cash date, the accounting recognition period, and the actuarial grouping period distinct.

This exercise brings together those distinctions. It uses simple, explicitly stated transactions and straight-line earning for uniform coverage. The loss and expense amounts are given as recognized amounts; the calculations do not estimate ultimate claims or develop unpaid liabilities. The concepts are aligned with the CAS Exam 5 (Basic Ratemaking and Estimated Claim Liabilities) syllabus.

Definition: A calendar-year (CY) view groups activity by calendar-year accounting or cash dates, as specified. A policy-year (PY) view groups policies by their effective-date year. An accident-year (AY) view groups losses by the year in which the covered event occurred. These periods need not contain the same transactions or amounts.

A Transaction-by-Transaction Framework

For each item, identify what happened, when cash moved, and when the related income or expense belongs in the accounts. Then identify whether a policy-year or accident-year grouping is relevant. A cash payment is not automatically a current-period expense, and a cash receipt is not automatically current-period earned premium.

Record the event and cash date.
For a premium, claim, or expense, note whether cash was received or paid and on what date.

Assign the accounting period.
Recognize premium as coverage is provided, claims in the period of occurrence when the recognized loss amount is given, and expenses as the related service is received.

Assign the actuarial period.
Use policy inception to assign a policy year and loss occurrence to assign an accident year.

Reconcile totals.
Compare recognized income and expenses with cash flows, accounting for amounts earned or incurred in a different period.

For a policy with uniform exposure over its term, a simple pro-rata allocation is appropriate. If a policy has premium $P$, a term of $n$ equal months, and $m$ months of coverage provided by the accounting date, then:

\text{Earned premium}=P\frac{m}{n}, \qquad \text{Unearned premium}=P-\text{Earned premium}.

The justification is that, under the stated uniform-coverage assumption, each month contributes the same share of the premium: $P/n$. Providing $m$ months of coverage therefore earns $m(P/n)$. This allocation does not assert that risk is always uniform; a different exposure pattern or earning convention may require a different allocation.

Worked Example: A Policy Crossing the Accounting Year

A hypothetical equipment policy has a $1,800 premium, is effective April 1, 2025, and covers the 12 months through March 31, 2026. The full premium is collected on April 1. Coverage is assumed uniform by month. A covered loss occurs September 10, 2025, and the recognized claim amount is $480. The insurer pays $200 on November 15, 2025, with the remaining $280 unpaid at December 31. Find the 2025 earned premium, year-end unearned premium, 2025 paid and incurred loss amounts, and the policy’s year assignments.

Premium earning. Nine months of coverage, April through December, have been provided by December 31. The earned fraction is $9/12$, so earned premium is $1{,}800(9/12)=\$1{,}350$. The unearned portion is $1{,}800-1{,}350=\$450$.

Claim amounts by view. The loss occurred in 2025, so the recognized $480 is a 2025 incurred loss and belongs to accident year 2025. Only $200 was paid in 2025, so the 2025 paid loss is $200. The unpaid $280 is the difference between the recognized claim amount and payment: $480-200=\$280$.

Policy-year assignment. The policy began in 2025, so its premium and covered claim belong to policy year 2025. The policy-year assignment does not change the fact that only $1,350 of its premium has been earned by year-end.

Check. Earned plus unearned premium equals the full premium: $1{,}350+450=1{,}800$. Paid plus unpaid claim amount equals the recognized claim: $200+280=480$. The common mistake is to call the entire $1,800 collected “2025 earned premium”; collection is a cash event, while earning follows coverage provided.

Policy-Year and Accident-Year Views

Policy year and accident year answer different grouping questions. A policy-year result follows the policies written in a given inception year, including their associated covered losses as those losses occur. An accident-year result follows losses by the year of occurrence, regardless of when the policy was written. A calendar-year paid-loss total instead follows when claim payments are made.

Worked Example: Assigning Premium and Losses to Different Years

Consider two hypothetical policies. Policy X begins November 1, 2024, has a 12-month term, and has a premium of $1,200. It has a $250 covered loss on January 20, 2025, of which $100 is paid in 2025. Policy Y begins March 1, 2025, has a 12-month term, and has a $1,800 premium. It has a $500 covered loss on December 10, 2025, paid in full during December. Assume uniform monthly coverage. Determine policy-year premium assignments, earned premium through December 31, 2025, accident-year incurred loss, and calendar-year paid loss.

Policy-year premium. Policy X began in 2024, so its $1,200 written premium belongs to PY2024. Policy Y began in 2025, so its $1,800 written premium belongs to PY2025.

Earned premium through year-end. Policy X provides 10 months of coverage in 2025, January through October. Its 2025 earned premium is $1{,}200(10/12)=\$1{,}000$. Policy Y provides 10 months of coverage in 2025, March through December. Its 2025 earned premium is $1{,}800(10/12)=\$1{,}500$. Total earned premium in calendar 2025 is $1{,}000+1{,}500=\$2{,}500$.

Accident-year incurred loss. Both losses occur in 2025. The AY2025 incurred loss is $250+500=\$750$, including the $250 loss on the policy written in 2024.

Calendar-year paid loss. The payment on Policy X is $100, and Policy Y’s payment is $500. Therefore CY2025 paid loss is $100+500=\$600$. The unpaid portion of X’s loss is $250-100=\$150$, so paid loss is not the same as incurred loss.

Check. The calendar-year earned premium is $2,500, not the sum of the two written premiums, $3,000. AY2025 incurred loss is $750, while CY2025 paid loss is $600. The common mistake is to exclude Policy X’s loss from AY2025 because the policy began in 2024; accident-year assignment follows occurrence, not policy inception.

Integrated Calendar-Year Accounting and Cash Reconciliation

The next example combines premiums, claims, and operating expenses in one hypothetical calendar-year ledger. A simple underwriting result is earned premium less incurred claims and incurred operating expenses. Cash flow instead uses actual receipts and payments. Reconciling the two requires tracking what remains unearned, unpaid, prepaid, or accrued at the period boundary.

Worked Example: Reconciling a Calendar-Year Result to Cash

A hypothetical insurer has the following 2025 transactions and opening balances. Policy A begins January 1, 2025, covers one year, and has a $1,200 premium collected at inception. Policy B begins July 1, 2025, covers one year, and has a $2,400 premium collected at inception. Coverage is uniform by month. A $900 loss occurs under Policy A in September 2025; $300 is paid in December. A $500 loss occurs under Policy B in November 2025 and is paid in January 2026. At January 1, 2025, the insurer also has an $800 claim from a 2024 accident, which it pays in February 2025.

The insurer also pays $300 in 2025 for operating services received in 2025. It pays $1,200 on October 1 for a software service covering October 1, 2025, through September 30, 2026. Software cost is recognized evenly over those 12 months. Finally, $400 of December 2025 payroll is paid in January 2026. Assume there are no other transactions or opening prepaid or accrued operating expenses. Calculate the 2025 underwriting result and net cash flow.

1. Earned premium. Policy A provides all 12 months of coverage in 2025, so it earns $1{,}200(12/12)=\$1{,}200$. Policy B provides six months, July through December, so it earns $2{,}400(6/12)=\$1{,}200$. Total 2025 earned premium is $\$1{,}200+\$1{,}200=\$2{,}400$. Total premium cash received is $1{,}200+2{,}400=\$3{,}600$. The $1,200 difference is premium collected for coverage after December 31; it is unearned at year-end.

2. Incurred and paid claims. The two 2025 accidents have recognized claim amounts of $900 and $500, so 2025 incurred loss is $900+500=\$1{,}400$. The current-year claim payments are $300 in December and $0 in 2025 on the November claim. The insurer also pays $800 for the 2024 accident. Thus total CY2025 paid loss is $300+800=\$1{,}100$, but the $800 payment relates to a prior accident year, not 2025 incurred loss.

At year-end, the unpaid portion of the September claim is $900-300=\$600$, and the unpaid November claim is $500. The closing claim liability from these given amounts is $600+500=\$1{,}100$. The opening liability of $800 was paid in 2025. The roll-forward checks: opening liability $800$, plus 2025 incurred claims $1{,}400$, less 2025 claim payments $1{,}100$, equals closing liability $1{,}100$.

3. Incurred and paid operating expenses. The $300 service cost is both paid and incurred in 2025. The software service covers three months of 2025, so its recognized 2025 expense is $1{,}200(3/12)=\$300$; the remaining $1{,}200-300=\$900$ is prepaid for 2026. The December payroll is a 2025 expense of $400 even though it is paid in 2026. Therefore 2025 incurred operating expense is $300+300+400=\$1{,}000$, while 2025 operating expense cash payments are $300+1{,}200=\$1{,}500$.

4. Underwriting result. Subtract incurred claims and incurred operating expenses from earned premium:

2{,}400-1{,}400-1{,}000=\$0.

5. Net cash flow. Premium receipts are $3,600. Claim payments are $1,100, and operating expense payments are $1,500. Net cash flow is therefore $3{,}600-1{,}100-1{,}500=\$1{,}000$.

6. Reconcile. Cash flow exceeds the underwriting result because premium cash includes amounts not yet earned, while claim and expense cash payments do not match current-period incurred costs. In this example:

\begin{aligned} \text{Net cash flow} &=\text{underwriting result} +(\text{premium received}-\text{premium earned})\\ &\quad+(\text{claims incurred}-\text{claims paid}) +(\text{expenses incurred}-\text{expenses paid})\\ &=0+(3{,}600-2{,}400)+(1{,}400-1{,}100)+(1{,}000-1{,}500)\\ &=0+1{,}200+300-500\\ &=\$1{,}000. \end{aligned}

The reconciliation also checks through period-end balances: the $1,200 unearned premium and $300 net increase in claim liabilities add to cash relative to the underwriting result; $400 accrued payroll less $900 prepaid software reduces it by $500. Thus $0+1{,}200+300+400-900=\$1{,}000$. The common mistake is to subtract all $1,100 of CY paid claims from 2025 earned premium as if it were 2025 incurred loss. The $800 payment settles an opening, prior-year claim liability.

Common Traps in an Integrated Period Exercise

Mixing cash and recognition. Premium collection does not establish that the premium is earned; a claim payment does not establish that the loss occurred in the payment year.
Using one year label for every amount. A 2025 payment may settle a 2024 accident, and a policy written in 2024 may have a 2025 accident.
Ignoring boundary balances. Unearned premium, unpaid claims, prepaid services, and accrued expenses explain why cash and accounting results differ.
Applying pro-rata earning without its assumption. The monthly fraction is appropriate here because uniform coverage and equal monthly earning were specified. It is not a universal rule for all policies.
Calling paid loss “incurred loss.” Keep the two measures separate unless the facts establish that the payment and recognized claim amount are equal in the same period.

Key takeaway: A reliable period analysis labels each amount by both its basis and its period: premium received versus earned, claim paid versus incurred, and expense paid versus incurred. Only after those labels are clear should the amounts be compared or reconciled.

Check Your Understanding

For each problem, keep cash dates, recognition periods, and actuarial groupings separate.

A uniform 12-month policy begins October 1, 2025, with a premium of $2,400 collected at inception. How much is earned in 2025, and how much is unearned on December 31? (Answer: earned premium $600; unearned premium $1,800.)
A $700 covered loss occurs December 20, 2025, and is paid $250 in January 2026. State the accident year, CY2025 paid loss, CY2025 incurred loss, and unpaid amount at December 31, assuming the full $700 is recognized in 2025. (Answer: AY2025; CY2025 paid loss $0; CY2025 incurred loss $700; unpaid $700.)
Policy M begins September 1, 2024, with a 12-month term and a $1,200 premium. A $300 covered loss occurs in February 2025. To which policy year and accident year does the loss belong? (Answer: PY2024 and AY2025.)
An insurer receives $5,000 of premium cash and earns $3,600. It incurs $1,100 of claims and pays $800, and incurs $500 of expenses while paying $650. If its underwriting result is earned premium less incurred claims and expenses, calculate the result and net cash flow. (Answer: underwriting result $2,000; net cash flow $3,550.)
A policy begins January 1, 2025, covers 12 uniform months, and has a $1,440 premium. A $600 loss occurs in December 2025, with $200 paid in December and $400 paid in February 2026. State the 2025 earned premium, 2025 incurred loss, 2025 paid loss, and policy and accident years. (Answer: earned premium $1,440; incurred loss $600; paid loss $200; PY2025 and AY2025.)

What You'll Learn