Cumulative Loss Payments through Development Month
Accident Year	Earned Premium	Expected Loss Ratio	12	24	36
AY1	9,500	0.7	5,250	6,700	7,500
AY2	10,000	0.72	5,250	7,300
AY3	11,500	0.75	6,550

There is no development past 36 months.

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

• 3,400
• 3,600
• 3,700
• 3,800
• 4,000

Solution: B

Step 1: Calculate year-to-year development factors

Development Factors

Months	Factor
12-24	(6,700 + 7,300)/(5,250 + 5,250) = 1.3333
24-36	7,500/6,700 = 1.1194

Step 2: Calculate expected losses for each accident year

Expected Loss

Accident Year	Expected Loss
AY2	10,000 *0.72 = 7,200
AY3	11,500 * 0.75 = 8,625

Step 3: Calculate the reserves for each accident year using the Bornhuetter-Ferguson method

Accident Year	Expected Loss	Cumulative Development Factor	Reserve
AY2	7,200	1.1194	(1-1/1.1194)*7,200 = 767.98
AY3	8,625	1.3333 * 1.1194 = 1.4925	(1-1/1.4925)*8,625 = 2,846.11
			Total: 3,614.09