You are given:

1. Earned premium in CY1 was 500,000.
2. Earned premium growth through CY3 has been constant at 10% per year (compounded).
3. The expected loss ratio for AY1 is 40%.
4. As of December 31, CY3, the expected loss ratio has increased 3 percentage points each accident year
5. Selected incurred loss development factors are as follows:

12 to 24 months	1.25
24 to 36 months	1.2
36 to 48 months	1.1
48 to 60 months	1.07
60 to 72 months	1.05
72 to ultimate	1.000

Calculate the total IBNR reserve as of December 31, CY3 using the Bornhuetter-Ferguson method.

• 5,800
• 6,000
• 6,300
• 6,600
• 6,900

Solution: A

We compute:

Year	Earned Premium	Expected Loss Ratio	Expected Loss	Cumulative Development Factor	Reserve
AY1	500,000	0.4	200,000	1.1 * 1.07 * 1.05 = 1.2356	(1-1/1.2356) * 200,000 = 38,135.32
AY2	550,000	0.43	236,500	1.2 * 1.1 * 1.07 * 1.05 = 1.483	(1-1/1.483) * 236,500 = 77,025.96
AY3	605,000	0.46	278,300	1.25 * 1.2 * 1.1 * 1.07 * 1.05 = 1.8534	(1-1/1.8534) * 278,300 = 128,143.5
					Total: 243,305