[[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