How Policy Terms Earn Premium

How Premium Becomes Earned

A policy’s written premium is recorded when the policy is issued or renewed, but the insurer provides coverage over the policy term. As that coverage is provided, the written premium is treated as earned. For experience analysis, the relevant question is often not how much premium was written, but how much of it was earned by a particular cutoff date.

For example, if an annual policy is in force for only part of an experience period, the full written premium does not belong in that period as earned premium. The calculation must reflect the part of the policy term that overlaps the period. This requires a clear term start, term end, cutoff date, and time-measure convention.

Definition: Written premium is premium recorded for a policy or a set of policies when written. Earned premium is the portion of written premium allocated to coverage already provided. Unearned premium is the portion allocated to coverage that has not yet been provided. Under a straight-line earning assumption, earned plus unearned premium equals the written premium for the policy.

Earning is an allocation over the coverage term. It is not determined by when the policyholder pays an installment, when the insurer receives cash, or when a claim occurs. A policyholder might pay in installments while the policy’s premium is still earned over the full term.

Straight-Line Earning Over a Policy Term

A common assumption for basic premium allocation is that coverage is provided uniformly over time. Under this assumption, premium is earned at a constant rate per unit of time. For a policy written for premium $W$, with term length $T$, the earned premium at a cutoff is based on the portion of the term that has elapsed.

\text{Earned fraction} = \frac{\text{elapsed covered time}}{\text{total policy-term time}}

\text{Earned premium} = W \times \text{earned fraction}, \qquad \text{Unearned premium} = W-\text{earned premium}.

Elapsed time must be capped at the policy term. Before a policy begins, it has earned no premium; after it expires, it has earned all of its written premium. For date-based calculations, a precise convention avoids ambiguity: treat a policy as covering the half-open interval from its inception date up to, but not including, its expiration date. Treat the cutoff as the start of the stated date. Thus, the elapsed time through a cutoff is the date difference between inception and cutoff, limited to the policy term.

Assumption and limitation: Straight-line earning assumes that coverage is provided uniformly per unit of time. It is a standard allocation convention for many ratemaking calculations, but it may not accurately represent coverage whose risk varies materially over the term. A special cancellation provision, such as a short-rate penalty, can also make the premium returned on cancellation differ from straight-line unearned premium.

The justification is direct. If $W$ dollars of premium are allocated evenly over $T$ units of time, the earning rate is $W/T$ dollars per unit. After $e$ units have elapsed, the earned amount is $e(W/T)$, so the earned fraction is $e/T$. The unearned amount is what remains:

\text{Earned premium} = e\left(\frac{W}{T}\right) = W\frac{e}{T}, \qquad \text{Unearned premium} = W\left(1-\frac{e}{T}\right).

If the experience period is a window rather than a period running from policy inception to a cutoff, count only the time common to both intervals. In other words, a policy contributes earned premium to the experience period only while it is both in force and within that period.

\text{Earned premium in }[a,b) = W \times \frac{ \max\!\left(0,\ \min(b,t_0+T)-\max(a,t_0)\right) }{T},

where $t_0$ is the policy inception date, $t_0+T$ is its expiration date, and the time differences use the same convention throughout. This overlap formula gives zero if the policy and experience period do not overlap.

Choosing a Consistent Time Convention

For day-based pro rata earning, calculate the actual number of days in the policy term and the actual number of covered days through the cutoff. Divide those two counts. Leap years matter because they can change the number of days in a term. A monthly convention can instead allocate premium by months or fractions of months, if that is the specified convention; it should not be mixed with an actual-day calculation partway through.

Annual, six-month, and other short-term policies follow the same principle. The denominator is the length of the policy term, not automatically 365 days or 12 months. For a short-term policy, using a full-year denominator would understate the rate at which its premium is earned.

Worked Example: An Annual Policy Through a September Cutoff

A hypothetical annual policy has written premium of $1,460. Its term is January 1, 2025, to January 1, 2026. Calculate its earned and unearned premium as of the start of September 1, 2025, using actual days and straight-line earning.

Method. Use actual-day pro rata earning. The policy term contains 365 days. From January 1 to September 1 is 243 days, so the coverage provided before the cutoff is 243 days.

Step 1: Find the daily earning amount. Divide the written premium by the full term length:

\frac{\$1{,}460}{365}=\$4\text{ per day}.

Step 2: Calculate earned premium. Multiply the daily amount by 243 elapsed days:

243 \times \$4=\$972.

Step 3: Calculate unearned premium and check.

\$1{,}460-\$972=\$488, \qquad \$972+\$488=\$1{,}460.

The policy has earned $972 and has $488 unearned as of the cutoff. The check confirms that earned and unearned premium sum to the written premium. A common mistake is to count September 1 as an additional covered day even though the cutoff is defined as the start of that date.

Worked Example: Earning a Six-Month Policy

A hypothetical six-month policy has written premium of $1,810 and runs from January 1, 2025, to July 1, 2025. Calculate the earned and unearned premium as of the start of April 1, 2025, using actual days.

Method. Apply straight-line actual-day earning to the stated six-month term. The term has $31+28+31+30+31+30=181$ days. The elapsed time from January 1 to April 1 is $31+28+31=90$ days.

Step 1: Determine the amount earned per day.

\frac{\$1{,}810}{181}=\$10\text{ per day}.

Step 2: Calculate earned premium through the cutoff.

90 \times \$10=\$900.

Step 3: Find the unearned amount and verify the allocation.

\$1{,}810-\$900=\$910, \qquad \$900+\$910=\$1{,}810.

The policy has earned $900 and has $910 unearned at the cutoff. The mistake to avoid is dividing by 365 simply because the policy is an insurance policy. Its premium is allocated over its 181-day term, not over a year.

Worked Example: A Two-Year Policy That Crosses a Leap Day

A hypothetical two-year policy runs from January 1, 2024, to January 1, 2026, and has written premium of $7,310. Calculate the earned premium as of the start of January 1, 2025, using actual days.

Method. Use the actual length of the full policy term and the actual elapsed time to the cutoff. The policy term includes February 29, 2024.

Step 1: Count the term days and elapsed days. The two-year term has 731 days: 366 days in 2024 and 365 in 2025. The elapsed period from January 1, 2024, to January 1, 2025, is 366 days.

Step 2: Calculate the earning rate and earned premium.

\frac{\$7{,}310}{731}=\$10\text{ per day}, \qquad 366 \times \$10=\$3{,}660.

Step 3: Calculate and check the unearned amount.

\$7{,}310-\$3{,}660=\$3{,}650, \qquad \$3{,}660+\$3{,}650=\$7{,}310.

The policy has earned $3,660 and has $3,650 unearned. A tempting but incorrect shortcut is to call the cutoff exactly halfway through the two-year term and assign half the premium, or $3,655. Actual-day pro rata earning is not half here: 366 of 731 days have elapsed.

Premium Earned During an Experience Period

A cutoff calculation from inception is useful when measuring earned premium to date. When the experience period begins after a policy has started, however, only the days within both the experience period and policy term count. For a group of policies, perform the allocation policy by policy and add the resulting earned amounts. Policies that have expired before the experience period contribute no premium to it; policies that begin after the period ends contribute none either.

Worked Example: Combining Policies With Different Terms

A hypothetical experience period is January 1 through April 1, 2025, interpreted as the interval from the start of January 1 to the start of April 1. Policy A has premium of $1,200 and runs from January 1, 2025, to January 1, 2026. Policy B has premium of $900 and runs from February 1, 2025, to August 1, 2025. Calculate the total premium earned in the experience period using actual-day pro rata earning.

Method. For each policy, calculate the overlap in days between its term and the experience period, then apply that fraction to its written premium.

Policy A. The experience period overlaps Policy A for 90 days, from January 1 to April 1. Its 365-day term gives:

\$1{,}200 \times \frac{90}{365} = \$295.8904\ldots = \$295.89.

Policy B. The overlap is from February 1 to April 1, or 59 days: 28 days in February and 31 days in March. The six-month term is 181 days. Therefore:

\$900 \times \frac{59}{181} = \$293.3701\ldots = \$293.37.

Total and check. Add the policy amounts, rounding each to cents:

\$295.89+\$293.37=\$589.26.

The experience period contains $589.26 of earned premium from these two policies. The key trap is to include all of Policy B’s premium merely because it was written during the experience period. Only 59 of its 181 term days overlap the period.

Common Mistakes and Practical Limits

Counting written premium as earned immediately. Written premium is associated with the policy when written; earned premium accumulates as coverage is provided.
Using the wrong denominator. Divide by the actual policy-term length under the chosen convention, not by a default year when the policy is shorter or longer.
Mixing time conventions. Do not calculate elapsed days but divide by the term in months. Use actual days throughout or use a specified monthly allocation consistently.
Ignoring the experience-period boundary. For a period that starts after inception, count only term days that overlap that period.
Assuming straight-line earning fits every risk. It is an allocation assumption, not a statement that the insured risk is truly constant. Material seasonal variation or special policy provisions may require a different treatment.

Key takeaway: Under straight-line earning, a policy contributes written premium in proportion to the part of its term that has elapsed or overlaps the experience period. Define the dates and time convention first, use the policy’s full term as the denominator, and check that earned plus unearned premium equals written premium.

Check Your Understanding

For each problem, use the stated day-count convention and assume straight-line earning. Treat the cutoff as the start of the stated date.

A hypothetical annual policy has written premium of $3,650 and runs from January 1, 2025, to January 1, 2026. Find the earned premium and unearned premium as of July 1, 2025. (Answer: $1,810 earned; $1,840 unearned.)
A hypothetical 90-day policy has written premium of $900 and runs from May 10, 2025, to August 8, 2025. Find the earned premium as of June 10, 2025, and state the unearned amount. (Answer: $310 earned; $590 unearned.)
A hypothetical policy has written premium of $1,820 and runs from October 1, 2024, to April 1, 2025. Using actual days, find the amount earned as of January 1, 2025. (Answer: $920.)
A hypothetical two-year policy has written premium of $7,310 and runs from January 1, 2024, to January 1, 2026. Using actual days, find the earned premium as of October 1, 2024. (Answer: $2,740.)
An experience period runs from January 1 to April 1, 2025. Policy A has premium of $1,200 and runs from January 1, 2025, to January 1, 2026. Policy B has premium of $900 and runs from February 1 to August 1, 2025. Using actual-day earning, calculate their combined earned premium in the experience period. (Answer: $589.26.)

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