You are given the following information on losses paid for each of AY1 through AY4:

			Incremental Loss Payments through Development Year
Accident Year	Earned Premium	Expected Loss Ratio	0	1	2	3
AY1	35,500	0.71	10,500	7,500	4,800	1,340
AY2	31,200	0.73	13,050	5,025	1,400
AY3	X	0.75	12,500	7,250
AY4	X + 5,000	0.75	18,400

The estimated loss reserve using the expected loss ratio method is 43,412.

Calculate X.

• 48,964
• 49,674
• 51,875
• 52,174
• 54,785

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

Key: A

Accident Year	Expected Ultimate Loss	Cumulative Paid-to-date	Reserve
AY1	35,500*0.71 = 25, 205	24,140	1065
AY2	31,200*0.73 = 22,776	19,475	3301
AY3	0.75X	19,750	0.75 X −19,750
AY4	0.75( X + 5000)	18,400	0.75( X + 5000) −18,400

43,412 = 1065 + 3301 + 0.75 X −19,750 + 0.75( X + 5000) −18,400 [math]\Rightarrow [/math] X = 48,964

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