[[Actuarial Notes Wiki|Wiki]] / [[Exam 5 (CAS)]] / **Earned Premium** ## Definition ==Earned Premium== is the portion of written premium that applies to coverage that has already been provided, calculated as the premium earned during a specific time period. ## Calculation ``` Earned Premium = Written Premium - Δ Unearned Premium Reserve For a single policy: Earned Premium = (Days Elapsed / Total Days) × Written Premium Example: 12-month policy, $1,200 premium After 3 months: $1,200 × (3/12) = $300 earned ``` ## Relationship to Written Premium ``` Calendar Year Earned = + Beginning Unearned Premium Reserve + Written Premium during year - Ending Unearned Premium Reserve ``` ## Uses in Ratemaking ``` Loss Ratio = Incurred Losses / Earned Premium Earned premium matches exposure period: - Premium for time coverage was provided - Matches period when losses could occur - Appropriate denominator for loss ratios ``` ## Example ``` Policy effective: 7/1/2024 Policy term: 12 months Written premium: $1,200 As of 12/31/2024: Elapsed: 6 months Earned: $1,200 × (6/12) = $600 Unearned: $600 (for coverage in 2025) ``` ## Related Concepts - [[Written Premium#Definition]] - [[On-Level Premium#Definition]] - [[Loss Ratio Method#Definition]] ## References - Werner & Modlin, Chapter 3