An insurance company uses the following information to set new rates:

1. The projected loss cost grows at an annual effective rate of 7% per year.
2. The table below shows loss cost data for two policy years, with corresponding weights:

   Policy Year	Loss Cost	Weight
   PY3	600	1 – p
   PY4	670	p

3. New rates will be effective on April 1, CY9. Policies are one-year policies and rates will be in effect for one year.

The projected expected loss cost is 951.

Calculate p.

• 0.089
• 0.119
• 0.567
• 0.881
• 0.911

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

Key: D

For any given policy year, the average accident date is a full year after the beginning of that year. Similarly for new rates effective on April 1, CY9, the midpoint of the effective period is April 1, CY10.

Therefore, the PY3 and PY4 loss costs will be projected 6.25 and 5.25 years, respectively.

Using the projected loss cost, we find:

[[math]] 600(1.07)^{6.25} (1 − p) + 670(1.07)^{5.25} (p) = 951 \Rightarrow p = 0.8813 [[/math]]

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