Gross Premium
Premium that covers claims plus an expense/profit load.
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Example
PP=$400, e=0.3: GP ≈ $571
How it works
The pure premium is the amount needed to pay expected claims, but an insurer also has to fund expenses such as commissions, admin, and profit margin. If the expense ratio is e, then only the remaining fraction (1 - e) of the gross premium is available to cover claims, so dividing the pure premium by that fraction gives the full charge. This is why the gross premium is larger than the pure premium whenever expenses are positive.
When to use it
Use this when pricing insurance policies or converting an expected claim cost into the premium customers should actually pay. It is especially useful in ratemaking, budgeting, and simple premium-loading calculations.
Worked example, step by step
Pure premium (PP) = $750 Expense ratio (e) = 0.20 Gross premium formula: GP = PP / (1 - e) Substitute the values: GP = 750 / (1 - 0.20) Simplify the denominator: GP = 750 / 0.80 Calculate: GP = 937.50 Final answer: The gross premium is $937.50
Common mistakes to avoid
- Using the expense ratio itself as the premium load instead of dividing by (1 - e)
- Entering e as 20 instead of 0.20
- Treating the formula as valid when expenses exceed 100% of premium, which would make the denominator zero or negative
Did You Know?
The expense ratio bundles commissions, admin and profit into the premium you actually pay.
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