Earned and Unearned Premium

Why Premium Is Earned Over Time

A premium may be charged for coverage that extends over a period of time. If the policyholder pays the full amount at the start, the insurer has received the money before providing all the coverage it relates to. As coverage is provided, part of the premium is considered earned. The portion relating to coverage still in the future is unearned.

The distinction is about the coverage provided, not simply when the money is paid. Paying a premium in full at the start does not make the entire amount earned immediately. Similarly, a premium paid in installments can still relate to coverage over a defined term. The allocation method depends on the earning basis assumed or specified for the policy.

A useful starting point is to distinguish premium charged for a policy term from premium earned to date. The amount charged for the term is often called the written premium. It is not necessarily equal to the earned premium at a particular point in the term. For example, if an annual premium is paid in advance, the amount written may be the whole annual premium even though only a fraction has been earned after a few months.

These amounts are not a measure of claims, profit, or the insurer's actual costs. They allocate premium to coverage provided and coverage remaining. Unless a problem says otherwise, calculations below assume a hypothetical policy with a fixed premium, no taxes or other charges, and no midterm changes to its coverage.

Straight-Line Earning

For a simple policy with a uniform earning basis, premium is allocated evenly over the policy term. If the full term is \(T\) days and \(t\) days of coverage have been provided, the earned fraction is \(t/T\). This is a time-based, or straight-line, allocation. If the premium is \(P\), the earned amount is \(P(t/T)\), and the unearned amount is the balance.

Here \(0\leq t\leq T\). At the start, \(t=0\), so none of the premium has been earned under this basis. At the end, \(t=T\), so the full premium has been earned. For a term measured in months, the same calculation can use months if the premium is assumed to be earned uniformly by month.

Why the Straight-Line Formula Holds

The formula follows from the assumption that each equal unit of time earns an equal share of the premium. Divide the full premium \(P\) into \(T\) equal daily shares. Each day corresponds to \(P/T\) of premium. After \(t\) days, the allocated amount is \(t\) such shares. The remaining \(T-t\) days correspond to the unearned balance.

This reasoning depends on the uniform earning assumption. If the amount of covered exposure differs substantially across the term and the problem specifies earning by exposure, elapsed time alone is not enough. In that case, allocate premium according to the stated exposure basis instead.

Unearned Premium and Cancellation Refunds

If coverage ends before the end of the term, some premium may relate to coverage that will not be provided. Under a pro-rata return arrangement, the refund is based on the unearned portion. But an unearned premium amount and a cancellation refund are not automatically the same thing. A contract may specify a cancellation charge, a different return-premium calculation, or no refund in a particular circumstance.

For a pro-rata cancellation with a uniform earning basis, the premium allocated to elapsed coverage is earned; the premium allocated to the remaining term is unearned. If a specified fee is deducted from the unearned amount, that changes the net refund, not the time-based calculation of earned premium. Do not assume that every contract uses pro-rata cancellation unless the problem says so.

When Time Alone Is Not the Earning Basis

Straight-line earning is appropriate when the problem assumes equal earning per unit of time. It is not a universal rule that coverage always earns premium at a constant rate. A problem may instead explicitly assign premium according to exposure units or a stated pattern over the term. If so, use that basis rather than replacing it with elapsed time.

Cancellation Terms Can Change the Refund

A pro-rata refund returns the time-based unearned amount under the assumed allocation. A contract may instead state a different cancellation formula. In a simple short-rate illustration, the contract might specify that a fixed percentage of the original premium is retained upon cancellation. That retained amount is a contractual return-premium result; it should not be confused with the amount earned by coverage under a separate straight-line allocation.

Common Mistakes

• Calling all prepaid premium earned. Payment timing does not determine the amount earned. Allocate premium according to coverage already provided.
• Reversing the elapsed and remaining fractions. For a straight-line term, elapsed time determines the earned fraction; remaining time determines the unearned fraction.
• Assuming every refund equals unearned premium. That equality holds only when the return arrangement gives a pro-rata refund with no deductions or adjustments.
• Using time when exposure is specified. If the problem gives an exposure-based earning pattern, allocate according to that pattern.
• Subtracting a fee from earned premium without instruction. A specified cancellation fee may reduce the refund while leaving the time-based earned and unearned allocation unchanged.