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Exercise

AAdmin
May 15'23

Answer

Key: C

Let P be the premium after the July 1, CY3 rate change. On November 15, CY5 the premium is 0.96P and on October 1, CY6 it becomes 1.05(0.96)P = 1.008P. The relevant parallelogram is:

% of policyearned100%50%0%CY3CY4CY5CY6CY77/1/CY37111/15/CY5-4210/1/CY6534

The upper left triangle for CY6 has area (1/2)(7/8)2 = 49/128 and the lower right triangle has area (1/2)(1/4)2 = 4/128. The weighted average is [49 + 4(1.008) + 75(0.960)]P/128 = 0.9768P. The current premium is 9200(1.008)/(0.9768) = 9494.

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

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