Insurance theory · page 3 of 10

Premiums

Written, earned and unearned premium, and exposure.

The same premium can be counted three ways, and each answers a different question. Mixing them up is the most common mistake in insurance reporting.

Written premium

Written premium is the full premium of every policy that starts in a period, counted the day it starts. It measures sales: how much business was booked.

Earned premium

An insurer only earns a premium as time passes and it carries the risk. A year's premium is earned day by day across the year:

\text{earned premium} = \text{premium} \times \frac{\text{days of cover in the period}}{\text{days in the term}}

Unearned premium is the rest: premium already received for cover still to come. It is a liability, because the insurer owes that cover (or a refund if the policy is cancelled).

A worked example

A Motor Comprehensive policy costs €1,200 and starts on 1 October 2025. In 2025 it gives 92 days of cover (1 October to 31 December), so:

\text{earned in 2025} = 1200 \times \tfrac{92}{365} = 302.47

Written premium in 2025 is the full €1,200; earned premium is €302.47; unearned at 31 December is €897.53, to be earned in 2026.

Billed premium

Customers may pay in monthly instalments (premium_transactions). Billing is about cash, not risk: a policy paid monthly and one paid up front earn exactly the same. Analysts sometimes use premium billed in a period as a quick stand-in for earned premium; it is close for a steady book, but it is not the same thing.

Use written premium to measure sales, earned premium to measure profitability, and never divide claims by written premium.

Exposure is the amount of risk carried, measured in policy-years: the same 92-day policy is policy-years of exposure in 2025. It is the denominator of claim frequency (see Measuring a portfolio).

Practise it on Day 4

Check your understanding

Answer every question, then check.

1. A €730 annual policy starts on 1 July 2025. How much is earned in 2025?

2. Which figure measures how much new business was sold?

3. Why is unearned premium a liability?

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