You are given the following earned premiums for three calendar years:

Calendar Year	Earned Premium
CY5	7,706
CY6	9,200
CY7	10,250

All policies have a one-year term and policy issues are uniformly distributed through each year.

The following rate changes have occurred:

Date	Rate Change
July 1, CY3	+ 7%
Nov. 15, CY5	– 4%
October 1, CY6	+ 5%

Rates are currently at the level set on October 1, CY6.

Calculate the earned premium at the current rate level for CY6.

• 9300
• 9400
• 9500
• 9600
• 9700

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

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:

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.