Company XYZ sells homeowners insurance policies. You are given:

1. The loss costs by accident year are:

   Accident Year	Loss Cost
   AY1	1300
   AY2	1150
   AY3	1550
   AY4	1800

2. The slope of the straight line fitted to the natural log of the loss costs is 0.1275.
3. AY4 experience is weighted 80% and AY3 experience is weighted 20% for rate development.

New rates take effect November 1, CY5 for one-year policies and will be in effect for one year.

Calculate the expected loss cost for these new rates.

• 2124
• 2217
• 2264
• 2381
• 2413

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

Key: E

Policies sold from November 1, CY5 to November 1, CY6 will be in effect through November 1, CY 7 and thus have an average accident date of November 1, CY6. For losses in AY4 the projection is 2.333 years and the projected cost is [math]1800e^{0.1275(2.333)} = 2423.58 [/math]. For losses in AY3 the projection is 3.333 years and the projected cost is [math]1550e^{0.1275(3.333)} = 2370.76 [/math]. The projected loss cost is the weighted average, (0.8)(2423.58) + (0.2)(2370.76) = 2413.02 = 2413.

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