Cancellation and the Premium for Unused Coverage
A cancellation ends an insurance policy before its scheduled expiration date. Because the insurer will not provide coverage after the cancellation takes effect, some premium may relate to a period of coverage that will not occur. Identifying that amount is the first step in determining whether premium may be returned to the policyholder.
The key distinction is between unearned premium and a cash refund. Unearned premium describes premium attributed to coverage after the cancellation date. A cash refund is an amount actually payable to the policyholder after applying the contract’s cancellation provisions and settling the policy account. Those amounts need not be equal.
The cancellation effective date matters: it identifies when future coverage stops. The exact treatment of the date itself—such as whether coverage ends at the start or end of that day—must follow the policy and the stated calculation convention. A calculation should never silently assume a date-counting rule that the problem has not supplied.
Cancellation is prospective. It ends coverage after the effective date; it does not, by itself, erase coverage for earlier dates or undo premium already earned. For example, a loss that occurred before cancellation is not made uncovered merely because the policy later ended, subject to the policy’s terms and other applicable conditions.
Relating Earned Premium to Unearned Premium
Let \(P\) denote the premium amount to which the stated earning basis applies, \(EP(t)\) the premium earned through time \(t\), and \(UEP(t)\) the unearned premium at time \(t\). If the full premium is divided between earned and unearned portions, with no adjustment to the premium amount, then:
Rearranging gives the basic relationship:
This identity follows from how the two portions are defined. The premium attributed to coverage already provided is the earned part; the premium attributed to remaining coverage is the unearned part. Together, those portions account for the premium in scope. A cancellation stops future coverage, so the unearned portion is a natural starting point for assessing a possible return.
The identity does not say that every dollar of unearned premium must be paid as a refund. The amount potentially returned depends on which premium components are subject to return and on the policy’s cancellation provisions. A fee may be nonrefundable; an amount owed may offset a credit; and the contract may specify a cancellation calculation that differs from simply returning the unearned portion on a uniform basis. Use only the rules and earning basis provided in the problem.
Worked Examples
Worked Example: Cancellation Under a Stated Daily Earning Basis
A hypothetical property policy has a 365-day term and a coverage premium of $1,200. Its terms allocate premium uniformly by coverage day. Cancellation is effective after 110 covered days have elapsed, with 255 days remaining. Assume the full premium was paid and there are no fees or other adjustments. Find the earned premium, unearned premium, and potential return under the stated basis.
Method. Apply the stated uniform daily earning basis to the elapsed and remaining coverage days. The common mistake this avoids is using the elapsed fraction to calculate the unearned amount.
First check the day counts: \(110+255=365\). The earned fraction is \(110/365\), so:
The unearned fraction is \(255/365\), so:
Rounding to the nearest cent only after calculating gives earned premium of $361.64 and unearned premium of $838.36. The check is \(361.64+838.36=\$1,200.00\). Since the full premium was paid and no deductions or other adjustments apply, the potential return under the stated basis is $838.36.
Worked Example: Separating Premium From a Nonrefundable Charge
A hypothetical 12-month policy has a coverage premium of $2,400 and a separate $150 policy charge. The policyholder paid $2,550 at inception. The contract states that the policy charge is not refundable and that the coverage premium is earned uniformly by month for purposes of this cancellation. Coverage ends after four complete months. Determine the coverage premium earned, the unearned coverage premium, and the amount potentially returned.
Method. Apply the cancellation basis only to the coverage premium, then treat the charge separately. The common mistake this avoids is applying the unearned fraction to every dollar collected.
Four of the 12 months have elapsed, so the earned fraction is \(4/12\). Earned coverage premium is:
Eight of the 12 months remain, so the unearned coverage premium is:
The two coverage portions reconcile: \(\$800+\$1,600=\$2,400\). The separate $150 charge is nonrefundable by the stated terms, so it is not included in the potential return. With the account fully paid and no other adjustments, the potential return is $1,600. The insurer retains $800 of earned coverage premium plus the $150 charge, for a total retained amount of $950; \( \$950+\$1,600=\$2,550\), the amount originally paid.
Worked Example: Unearned Premium Does Not Guarantee a Cash Refund
A hypothetical annual policy has a $1,500 premium, billed in full at inception. The policyholder has paid $600, leaving $900 unpaid on the account. The policy is cancelled after six months. Assume the coverage premium is earned uniformly by month, and the contract gives a full credit for unearned premium. There are no fees or other adjustments. Determine the unearned premium and the account settlement.
Method. Calculate the unearned premium first, then apply it as a credit to the policy account. The common mistake this avoids is treating the unearned amount as cash automatically payable to the policyholder.
Six of the 12 months have elapsed, so earned premium is:
The remaining six months produce unearned premium of:
The $750 unearned premium is a credit against the $900 still owed. After applying the credit, the balance due is \(\$900-\$750=\$150\). Thus, the policyholder receives no cash refund and still owes $150. As a check, the insurer’s total premium after settlement is the $600 already paid plus the $150 balance, or $750—the earned premium through cancellation.
From Unearned Premium to the Amount Returned
A practical cancellation calculation has two parts. First, determine the premium associated with coverage through the effective date and the premium associated with the remaining coverage, using the stated basis. Second, determine how the resulting credit interacts with the policy’s terms and account balance. Keeping these parts separate prevents an accounting amount from being mistaken for an immediate payment.
Identify when coverage ends, the premium amount being assessed, and the earning or cancellation basis specified by the problem.
Apply the stated basis to the coverage provided and remaining coverage. Check that the portions reconcile to the premium amount in scope.
Separate refundable premium from charges that are not refundable, and offset any credit against amounts still due as the stated terms require.
A final cash return can be zero even when unearned premium is positive, as the third example shows. Conversely, if the premium is fully paid, no nonrefundable amounts apply, and the contract returns the applicable unearned premium, the credit may be paid to the policyholder. The result depends on the facts, not on the word “unearned” alone.
The premium amount used also matters. If a policy has been changed by an endorsement or a premium audit, the amount currently applicable to the coverage may differ from the amount originally billed. Use the premium and transactions specified in the problem; do not assume that an original inception amount remains the correct basis after changes. The earlier material on earned premium and unearned premium provides the underlying distinction between coverage already provided and coverage remaining.
Common Mistakes and Why the Distinctions Matter
- Reversing elapsed and remaining coverage. A calculation based on elapsed coverage estimates earned premium; a calculation based on remaining coverage estimates unearned premium. Confirm which quantity is being requested.
- Ignoring the effective date convention. A day-count error changes the elapsed and remaining coverage. State or follow the convention before counting days.
- Applying a return basis to excluded charges. Confirm whether a charge is part of the premium subject to return. A collected amount is not automatically refundable premium.
- Calling a credit a refund. A credit may first reduce an unpaid balance. Calculate the account settlement before concluding that cash will be paid.
- Assuming every contract returns the full unearned amount. The policy’s provisions govern the cancellation adjustment. If the problem supplies a particular rule, use it; if it does not, avoid inventing one.
These distinctions matter because premium is tied to both coverage and accounting. A policy can stop providing future coverage while an account still has a balance to settle. Correctly identifying the unearned portion is therefore necessary, but not always sufficient, to determine the final transaction. This treatment of cancellation and premium measurement is aligned with the CAS Exam 5 (Basic Ratemaking and Estimated Claim Liabilities) syllabus.
Check Your Understanding
For each problem, use only the earning basis and cancellation terms stated. Round dollar amounts to the nearest cent where needed.
- A hypothetical policy has a $900 coverage premium for 365 days. It earns uniformly by day, and cancellation takes effect after 146 covered days, leaving 219 days. The full premium has been paid, and no other adjustments apply. Find the potential return. (Answer: $540.00)
- A hypothetical policy has a $1,800 coverage premium for 12 months. The policy states that premium is earned uniformly by month and allows return of the unearned premium. It is cancelled after five complete months, and the full premium has been paid. Find earned premium and potential return. (Answer: Earned premium $750; potential return $1,050)
- A hypothetical policy has a $2,400 coverage premium and a separate $100 nonrefundable charge. It is cancelled after three of 12 complete months under a uniform monthly earning basis; all amounts have been paid. Find the potential return and total amount retained. (Answer: Potential return $1,800; total retained $700)
- A hypothetical annual policy has a $1,200 premium billed in full. The policyholder has paid 30% of the bill. Cancellation occurs after eight months under a uniform monthly earning basis, and the contract credits all unearned premium against the account. Find the account balance after the credit and state whether cash is refunded. (Answer: $440 due; no cash refund)
- A hypothetical policy has a $1,500 premium. Its stated earning schedule allocates 60% of premium to the first six months and 40% to the final six months. It is cancelled at the end of month six, with the full premium paid and no other adjustments. Find earned and unearned premium and check the total. (Answer: Earned premium $900; unearned premium $600; total $1,500)