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Consider two companies, Company ABC and Company XYZ. Company ABC has a permissible loss ratio of 70%, which includes a margin for profit and contingencies

Consider two companies, Company ABC and Company XYZ. Company ABC has a permissible loss ratio of 70%, which includes a margin for profit and contingencies equal to 2.5% of gross premium. Company XYZ discounts all loss payments using a single discount factor of (1 + i) 1 2 for the calculation of the pure premium, but includes a margin for profit and contingencies equal to 5.5% of gross premium. All other quantities, including all other expenses, are the same for both companies. Determine i such that both companies have the same gross premiums. 

 

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