You are given the following loss data:

Size of Loss	Number of Claims	Ground-Up Total Losses
0 – 99	1100	58,500
100 – 249	400	70,000
250 – 499	300	120,000
500 – 999	200	150,000
> 999	100	200,000
Total	2100	598,500

Calculate the percentage reduction in loss costs by moving from a 100 deductible to a 250 deductible.

• 25%
• 27%
• 29%
• 31%
• 33%

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

Key: B

With no deductible, the loss cost is proportional to 598,500. With a 100 deductible it is proportional (in the same proportion) to 598,500 – 58,500 – 1000(100) = 440,000. With a 250 deductible it is 598,500 – 58,500 – 70,000 – 600(250) = 320,000. The reduction is 120,000/440,000 = 0.273 = 27%.

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