Reconciling Written, Earned, and Collected Premium

Why Premium Measures Differ

A policy can generate a premium transaction on one date, provide coverage over a different span of time, and generate cash on yet another date. As a result, written, earned, and collected premium for the same reporting period need not be equal. Each measure answers a different question: what premium was recorded as written, what value of coverage was provided, and what cash was received?

For a portfolio, the reconciliation depends on two balances at the beginning and end of the period: premium receivable and unearned premium. Receivables connect written premium to collections; unearned premium connects written premium to earned premium. Keeping these two connections separate is the safest way to avoid sign errors.

Definition: For a specified reporting period, written premium is premium recorded from policy transactions during that period; earned premium is the portion associated with coverage provided during that period; and collected premium is premium cash received during that period. Premium receivable is written premium billed but not yet collected, while unearned premium is written premium associated with coverage that remains after the reporting date.

These measures use different timing bases. Written premium follows the recording of premium transactions. Earned premium follows the passage of covered time, using the applicable earning approach. Collected premium follows the receipt of cash. The earlier material on written premium, earned premium, unearned premium, and cash receipts establishes these underlying measures; here the focus is how to reconcile them for a portfolio.

The Two Reconciliation Equations

Let $W$ denote written premium during the period, $E$ earned premium, and $C$ collected premium. Let $R_0$ and $R_1$ be premium receivable at the beginning and end of the period, respectively. Let $U_0$ and $U_1$ be unearned premium at the beginning and end of the period.

Under a consistent accounting basis, and assuming no write-offs or other adjustments to premium receivable, cash collected is the amount available from the current-period written premium and the opening receivable, less the amount still receivable at the close:

$$ C = W + R_0 - R_1 $$

The earned premium equation follows from the unearned-premium balance. Written premium increases the amount not yet earned, while earned premium reduces it. Thus the closing balance equals the opening balance plus written premium less earned premium:

$$ U_1 = U_0 + W - E $$

Rearranging gives the earned-premium reconciliation:

$$ E = W + U_0 - U_1 $$

Key result: To reconcile collected premium directly to earned premium, substitute $W=C-R_0+R_1$ into $E=W+U_0-U_1$. The result is

$$ E = C - R_0 + R_1 + U_0 - U_1 $$

The receivable signs are negative for the opening balance and positive for the closing balance. The unearned-premium signs are positive for the opening balance and negative for the closing balance.

Why the Signs Have This Pattern

The two equations can be justified by tracking how the balances move. For receivables, the opening balance is premium already written before the period but still owed. If it is collected during the period, it contributes to cash without being written again. Current-period written premium also contributes to the amount available for collection. Any amount remaining unpaid at the end is excluded from cash collected. That gives $C=W+R_0-R_1$.

For unearned premium, the opening balance represents coverage value still to be earned from earlier writing. Current-period written premium adds to the amount available to be earned, and the closing balance is what remains for future coverage. Subtracting that remaining amount leaves the earned premium for the period: $E=W+U_0-U_1$.

Combining the equations requires care with the receivable terms. From $C=W+R_0-R_1$, solve for written premium first:

$$ W = C - R_0 + R_1 $$

Then substitute this expression for $W$, without changing its signs, into the earned-premium equation:

$$ E = (C - R_0 + R_1) + U_0 - U_1 $$

This derivation also provides a useful check: if an opening receivable is larger, all else equal, some of the period's cash may relate to earlier writing, so less current written premium is implied by a given collection total. A larger closing receivable has the opposite effect because more current writing remains unpaid.

Worked Reconciliations

Worked Example: A Portfolio with Changing Balances

A hypothetical insurer reports the following amounts for one calendar year, in dollars: written premium of $1,800, opening premium receivable of $300, closing premium receivable of $450, opening unearned premium of $800, and closing unearned premium of $500. Calculate collected and earned premium, then verify the direct reconciliation.

Method. First reconcile written premium to collections, then reconcile written premium to earned premium. This keeps the balance movements separate.

Collected premium. Apply $C=W+R_0-R_1$:

$$ C = 1{,}800 + 300 - 450 = 1{,}650 $$

Thus, $1,650 was collected during the year. The amount is below written premium because the closing receivable exceeds the opening receivable by $150.

Earned premium. Apply $E=W+U_0-U_1$:

$$ E = 1{,}800 + 800 - 500 = 2{,}100 $$

Earned premium exceeds current-year written premium because $300 more unearned premium was released than added during the year.

Direct check. Substitute the collections and the four balances into the combined equation:

$$ E = 1{,}650 - 300 + 450 + 800 - 500 = 2{,}100 $$

The direct result agrees with the earned-premium calculation. A common mistake is to write $C+R_0-R_1$ as the written premium implied by collections. That reverses the receivable signs: the correct expression is $W=C-R_0+R_1$. With these data, the incorrect direct calculation would give $1{,}650+300-450+800-500=1{,}800$, not the earned premium of $2,100.

Worked Example: Coverage and Installment Timing

A hypothetical portfolio has two policies. At January 1, an existing policy has $600 of unearned premium and covers January through June; assume it earns evenly over those six months. A new policy begins October 1, has a one-year term, and has written premium of $1,200; assume it earns evenly by month. The opening premium receivable is $200. During the year, $200 of that opening receivable is collected, and the new policyholder pays $200 toward the new policy's billed premium. The closing receivable is $1,000. Calculate written, earned, and collected premium, and explain why they differ.

Written premium. Only the new policy is written during the year, so $W=\$1{,}200$.

Earned premium. The existing policy's entire opening unearned balance is earned during the first six months, contributing $600. The new policy is in force for three months of the year, October through December. Its earned portion is:

1{,}200 \times \frac{3}{12} = 300

Total earned premium is $600+300=\$900$. The new policy has $900 remaining unearned at year-end, so the balance check is:

E = W + U_0 - U_1 = 1{,}200 + 600 - 900 = 900

Collected premium. The two cash payments total $200+200=\$400$. The receivable equation independently verifies this:

C = W + R_0 - R_1 = 1{,}200 + 200 - 1{,}000 = 400

The $200 collected from the opening receivable relates to premium written before this year; it is not additional current-year written premium. The other $200 is a partial payment toward the new policy. The remaining $1,000 of the new premium is still receivable.

Direct check. Using the collected amount and both opening and closing balances:

$$ E = 400 - 200 + 1{,}000 + 600 - 900 = 900 $$

The check agrees. The key trap is treating the $400 collected as if it were either all current-year writing or all coverage earned; its timing does not establish either conclusion.

Worked Example: A Calendar-Year Portfolio Check

A hypothetical insurer has $900 of unearned premium at January 1 from an existing policy that expires September 30. During the year, it writes a $900 policy effective January 1 with a nine-month term and a $2,400 policy effective July 1 with a one-year term. Assume premiums earn evenly by month. Opening premium receivable is $250; during the year the insurer collects $250 of that balance and $1,450 from the current-year invoices. Calculate the three premium measures and verify them using closing balances.

Written premium. The two current-year transactions total:

$$ W = 900 + 2{,}400 = 3{,}300 $$

Earned premium. The opening policy's remaining coverage is entirely provided during the year, so it contributes $900. The new nine-month policy earns its full $900 by September 30. The July 1 annual policy earns six of twelve months:

2{,}400 \times \frac{6}{12} = 1{,}200

Therefore, earned premium is $900+900+1{,}200=\$3{,}000$. The July policy has $1,200 unearned at year-end; the other two policies have no remaining unearned premium. Thus $U_0=\$900$, $U_1=\$1{,}200$, and:

E = W + U_0 - U_1 = 3{,}300 + 900 - 1{,}200 = 3{,}000

Collected premium and closing receivable. Cash received is the opening-balance collection plus the current-invoice collection:

$$ C = 250 + 1{,}450 = 1{,}700 $$

The closing receivable is the opening receivable plus current writing less cash collected:

R_1 = R_0 + W - C = 250 + 3{,}300 - 1{,}700 = 1{,}850

Direct check. The combined equation gives:

$$ E = 1{,}700 - 250 + 1{,}850 + 900 - 1{,}200 = 3{,}000 $$

The check matches the policy-level earning calculation. Written premium of $3,300, earned premium of $3,000, and collected premium of $1,700 differ for distinct reasons: the year begins with coverage still to be earned, ends with coverage still unearned, and ends with a substantial amount still unpaid.

Practical Checks and Common Traps

A reconciliation is useful both as a calculation and as a data-quality check. When portfolio totals do not agree, inspect the period boundaries and the accounting definitions before assuming that a policy-level calculation is wrong.

Mixing cash and coverage timing. Collections do not determine when coverage was provided. A paid-in-full policy may be only partly earned at the reporting date.
Using the wrong receivable signs. The direct equation is $E=C-R_0+R_1+U_0-U_1$, not $C+R_0-R_1+U_0-U_1$. Solve the collection equation for $W$ before substituting.
Comparing inconsistent populations. Written premium, collections, and balances must use the same portfolio scope, reporting dates, and treatment of transactions. A missing policy or a balance from a different cutoff can break the reconciliation.
Ignoring adjustments outside the simple model. The displayed receivable equation assumes there are no write-offs, reclassifications, or non-premium cash amounts in the totals. If those occur, they must be separately identified and incorporated rather than forced into the basic equation.
Assuming a particular earning pattern without support. Monthly pro rata earning is appropriate only when the problem specifies or supports even earning over time. The reconciliation identity still holds when a different consistent earning method is used, but the earned amount and unearned balance must match that method.

A reliable workflow is to calculate $W$, $C$, and $E$ using the definitions appropriate to the data, then reconcile $W$ to $C$ through receivables and $W$ to $E$ through unearned premium. Finally, combine the two equations as an independent arithmetic check. This separation is aligned with the CAS Exam 5 (Basic Ratemaking and Estimated Claim Liabilities) syllabus, where premium measures must be interpreted consistently before they are used in ratemaking.

Check Your Understanding

For each hypothetical portfolio, use the stated beginning and ending balances for the same reporting period. Assume the basic reconciliations above apply.

A portfolio has written premium of $900, opening unearned premium of $300, and closing unearned premium of $150. What is earned premium? (Answer: $1,050.)
Written premium is $2,400, opening receivable is $500, and closing receivable is $700. What is collected premium? (Answer: $2,200.)
Collected premium is $1,500; opening and closing receivables are $200 and $400; opening and closing unearned premium are $600 and $300. Reconcile earned premium directly. (Answer: $2,000.)
A portfolio has written premium of $2,800, opening and closing unearned premium of $400 and $900, and opening and closing receivables of $350 and $650. Calculate both earned and collected premium. (Answer: earned premium is $2,300; collected premium is $2,500.)
Collected premium is $3,200, opening receivable is $600, closing receivable is $900, opening unearned premium is $1,000, and closing unearned premium is $700. First infer written premium, then calculate earned premium using both reconciliation equations. (Answer: written premium is $3,500; earned premium is $3,800.)

What You'll Learn