You are given:

1. Policies are written uniformly throughout the year.
2. Policies have a term of 6 months.
3. The following rate changes have occurred:

Date	Amount
October 1, CY1	+7%
July 1, CY2	+10%
September 1, CY3	–6%

Rates are currently at the September 1, CY3 level.

Calculate the on-level factor needed to adjust CY2 earned premiums to the current rate level.

• 0.97
• 0.98
• 0.99
• 1.00
• 1.01

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

Key: E

Let P be the premium prior to the October 1, CY1 rate change. After the change, the premium is 1.07P and on July 1, CY2 it becomes 1.10(1.07)P = 1.177P. The relevant parallelogram is:

The upper left triangle for CY2 has area (1/2)(1/4)(1/2) = 1/16 and the lower right triangle has area (1/2)(1/2)(1) = 4/16. The weighted average is [1 + 4(1.177) + 11(1.07)]P/16 = 1.092375P. The factor is (1.177×.94)/(1.092375) = 1.0128.

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