Cumulative Loss Payments through Development Month
Accident Year	Earned Premium	Expected Loss Ratio	12	24	36	48
AY5	19,000	0.90	4,850	9,700	14,100	16,200
AY6	20,000	0.85	5,150	10,300	14,900
AY7	21,000	0.91	5,400	10,800
AY8	22,000	0.88	7,200

There is no development past 48 months.

Calculate the indicated loss reserve using the Bornhuetter-Ferguson method and volume-weighted average loss development factors.

• 22,600
• 23,400
• 24,200
• 25,300
• 26,200

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

Key: B

The year-to-year development factors are 12-24: 30,800/15,400 = 2; 24-36: 29,000/20,000 = 1.45; and 36-48: 16,200/14,100 = 1.149. Then the factor for 24-48 is 1.45(1.149) = 1.666 and for 12-48 is 2(1.666) = 3.332.

The expected ultimate losses are AY6: 20,000(0.85) = 17,000; AY7: 21,000(0.91) = 19,110; and AY8: 22,000(0.88) = 19,360.

The B-F reserves are 17,000(1 – 1/1.149) = 2205, 19,110(1 – 1/1.666) = 7639, and 19,360(1 – 1/3.332) = 13,550.

The total is 23,394.