Written and Earned Premium at Different Rate Levels

Why Written and Earned Premium Differ

A premium can be recorded as written before the insurer has provided all of the coverage it buys. Conversely, a calendar period can contain earned premium from policies written in an earlier period. When policies have different effective dates, those distinctions also determine which rate level applies to each portion of the portfolio.

The key is to keep three dates conceptually separate: the date a policy is written, the date its coverage begins, and the dates on which coverage is provided. A rate-change date matters because it can determine the premium charged for a policy taking effect on or after that date. For the calculations below, assume hypothetical annual policies with premiums paid in full when written, no cancellations or endorsements, and uniform earning over each policy term. Where policies begin on the first of a month, use whole months to measure coverage.

Definition: Written premium is premium associated with policies written during a specified period, under the stated accounting convention. Earned premium is the portion of premium attributable to coverage provided during a specified period. A policy’s premium can be written in one period and earned across several periods.

Written and earned premium answer different questions. Written premium records premium from policy writings during the period. Earned premium measures the premium for insurance protection provided during the period. Neither is automatically a measure of the other, and a period’s earned premium need not come only from policies written during that period.

Assigning Premium to a Rate Level

A rate level identifies the pricing basis in effect under the stated rating rule. In the examples here, the hypothetical insurer assigns the policy’s rate level using its effective date: a policy effective before the stated change date is at the old level, and a policy effective on or after that date is at the new level. Actual rating rules may specify other details, so use the rule given in a problem rather than assuming that the issue date controls.

Once a policy’s premium and rate level are identified, earned premium for a calendar period is allocated according to the coverage the policy provides during that period. Under uniform earning for a 12-month policy, each covered month earns one-twelfth of the policy premium. For a set of policies, calculate each policy’s contribution separately before adding amounts. This preserves the connection between the earned premium and the rate level at which each policy was priced.

Formula under uniform earning: For an annual policy with written premium $P$, if $m$ of its 12 coverage months fall in the reporting period, the premium earned in that period is $P(m/12)$. This assumes coverage and premium are earned uniformly over the policy term; it is not a general rule for every policy or earning pattern.

The formula follows from allocating the premium evenly across the term. One month of a 12-month policy represents $1/12$ of its coverage. Under the uniform-earning assumption, it therefore earns $P/12$. For $m$ covered months in the reporting period, add $m$ equal monthly amounts:

\underbrace{\frac{P}{12}+\frac{P}{12}+\cdots+\frac{P}{12}}_{m\text{ covered months}} = \frac{mP}{12}.

This is an allocation of a given policy premium over time, not a method for adjusting historical premium to a new rate level. It also does not mean the whole policy premium is earned in the calendar year in which the policy is written.

Worked Examples

Worked Example: A Policy Crossing a Calendar-Year Boundary

A hypothetical annual policy is written and takes effect October 1, 2025, with a premium of $1,200. Its full term runs from October 1, 2025, through September 30, 2026. It is priced at the old rate level. Find its written premium in calendar year 2025 and its earned premium in calendar years 2025 and 2026.

Method. Record the full premium as written in the year the policy is written. Then allocate it to each calendar year by counting the policy’s coverage months in that year.

Written premium. The policy is written in 2025, so it contributes $1,200 to 2025 written premium. It contributes nothing to 2026 written premium under the assumption that there are no later writings or premium transactions.

Earned premium in 2025. The policy provides coverage in October, November, and December: 3 months. Its 2025 earned premium is $1{,}200(3/12)=\$300$.

Earned premium in 2026. The policy provides coverage from January through September: 9 months. Its 2026 earned premium is $1{,}200(9/12)=\$900$.

Check. The earned amounts total $\$300+\$900=\$1{,}200$, equal to the policy premium over its full term. Both earned amounts remain associated with the old rate level. The common mistake is to treat the $1,200 written in 2025 as all earned in 2025; that would ignore the nine months of coverage provided in 2026.

Worked Example: Written and Earned Premium in a Rate-Change Year

A hypothetical insurer changes rates effective January 1, 2026. Under the stated rule, policies effective before that date are priced at the old level, and policies effective on or after it are priced at the new level. Policy A is written and effective July 1, 2025, with an annual premium of $1,200. Policy B is written and effective January 1, 2026, with an annual premium of $1,500. Policy C is written and effective October 1, 2026, with an annual premium of $1,500. Find 2026 written premium and 2026 earned premium, with earned premium split by rate level.

Method. First determine which policies were written in 2026. Separately, count each policy’s coverage months falling in 2026. Assign rate level using each policy’s effective date.

2026 written premium. A was written in 2025 and contributes nothing to 2026 written premium. B and C were written in 2026, so written premium is $\$1{,}500+\$1{,}500=\$3{,}000$. Both are at the new rate level.

2026 earned premium from A. A’s July 1, 2025–June 30, 2026 term has January through June 2026 in the calendar year: 6 months. It earns $1{,}200(6/12)=\$600$, all at the old level.

2026 earned premium from B. B’s January 1–December 31, 2026 term has 12 months in 2026. It earns $1{,}500(12/12)=\$1{,}500$, at the new level.

2026 earned premium from C. C’s October 1, 2026–September 30, 2027 term has October through December 2026 in the calendar year: 3 months. It earns $1{,}500(3/12)=\$375$, at the new level.

Total and check. The old-level earned premium is $600; the new-level earned premium is $\$1{,}500+\$375=\$1{,}875$. Total 2026 earned premium is $\$600+\$1{,}875=\$2{,}475$. The $3,000 of 2026 written premium is not the 2026 earned premium: the former counts B and C in full when written, while the latter includes partial coverage from A and only partial-year coverage from C.

Worked Example: The Issue Date and Effective Date Point to Different Years

A hypothetical insurer changes rates effective January 1, 2026. Its stated rule assigns the rate level by policy effective date. Policy D is issued November 15, 2025, takes effect December 1, 2025, and has an annual premium of $960. Policy E is issued December 20, 2025, takes effect January 1, 2026, and has an annual premium of $1,440. Find 2025 written premium and 2026 earned premium by rate level.

Method. Use issue dates to identify the year of writing, but use effective dates to identify the rate level and the start of coverage. Then count coverage months in 2026.

2025 written premium. Both policies are issued in 2025. Therefore, 2025 written premium is $\$960+\$1{,}440=\$2{,}400$.

Rate levels. D takes effect before January 1, 2026, so it is at the old level. E takes effect on January 1, 2026, so it is at the new level. Although E is issued in 2025, its effective date places it at the new level under the problem’s rule.

2026 earned premium from D. D’s term runs from December 1, 2025, through November 30, 2026. Its 11 coverage months in 2026 earn $960(11/12)=\$880$, at the old level.

2026 earned premium from E. E provides coverage for all 12 months of 2026, so it earns $1{,}440(12/12)=\$1{,}440$, at the new level.

Total and check. Total 2026 earned premium is $\$880+\$1{,}440=\$2{,}320$. D earns its remaining $80 in December 2025, and E earns $1,440 over its full term from January through December 2026. The common mistake is to classify E at the old level because it was issued in 2025; that conflicts with the explicitly stated effective-date rule.

Reading the Results Correctly

A useful calculation should report both the period and the basis. “2026 premium” alone is ambiguous: it could mean premium written in 2026 or premium earned in 2026. If rate levels matter, report the earned premium at each level as well as the total. This makes visible whether the calendar period contains coverage priced under more than one level.

For example, the second worked example has $3,000 of 2026 written premium but $2,475 of 2026 earned premium. The written amount belongs to policies written during 2026. The earned amount includes coverage from a policy written in 2025, and excludes portions of 2026-written policies’ coverage that fall outside 2026. The difference is not an error; it reflects distinct timing definitions.

Key takeaway: Determine writing period from the date used to record the policy as written, determine earned premium from coverage provided during the reporting period, and assign rate level using the rating rule and relevant policy effective date. Keep these decisions separate until the final summary.

The uniform monthly formula applies only when the policy term and earning pattern support that allocation. If a problem specifies a different term, a nonuniform earning pattern, cancellations, endorsements, or other premium transactions, those details must be incorporated rather than silently applying $P(m/12)$. This distinction is aligned with the CAS Exam 5 (Basic Ratemaking and Estimated Claim Liabilities) syllabus: the calculation must match the exposure and premium timing being measured.

Check Your Understanding

For each problem, use the stated timing and uniform-earning assumptions. Separate written premium from earned premium where requested.

A hypothetical annual policy is written and effective September 1, 2025, with a premium of $1,800. How much does it contribute to 2025 written premium, and how much does it earn in 2026? (Answer: 2025 written premium $1,800; 2026 earned premium $1,200.)
A rate change takes effect May 1, 2026, and the stated rule assigns level by effective date. A policy is written and effective May 1, 2026, with annual premium $2,100. How much does it earn in 2026, and which level applies? (Answer: $1,400 earned at the new level.)
A policy effective November 1, 2025, has annual premium $900. Another effective March 1, 2026, has annual premium $1,200. Both are written on their effective dates, and a rate change takes effect January 1, 2026. Find 2026 earned premium by level and 2026 written premium. (Answer: $750 old-level earned; $1,000 new-level earned; $1,200 written.)
Policies A and B each have annual terms. A is issued November 15, 2025, effective December 1, 2025, and has premium $960. B is issued December 20, 2025, effective January 1, 2026, and has premium $1,440. The rate change is effective January 1, 2026, with level determined by effective date. Find 2025 written premium and 2026 earned premium. (Answer: 2025 written premium $2,400; 2026 earned premium $2,320, comprising $880 old-level and $1,440 new-level.)
A rate change is effective January 1, 2026, with level determined by effective date. Three policies are written on their effective dates: one effective August 1, 2025, with premium $1,200; one effective January 1, 2026, with premium $1,800; and one effective November 1, 2026, with premium $2,400. Find 2026 written premium and 2026 earned premium by level. (Answer: 2026 written premium $4,200; earned premium $700 old-level and $2,200 new-level, for total earned premium $2,900.)

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