You are given:

(i) An excerpt from a select and ultimate life table with a select period of 2 years:

[math]x[/math]	[math]l_{[x]}[/math]	[math]l_{[x]+1}[/math]	[math]l_{x+2}[/math]	[math]x+2[/math]
50	99,000	96,000	93,000	52
51	97,000	93,000	89,000	53
52	93,000	88,000	83,000	54
53	90,000	84,000	78,000	55

(ii) Deaths are uniformly distributed over each year of age

Calculate [math]10000_{2.2} q_{[51]+0.5}[/math].

• 705
• 709
• 713
• 1070
• 1074

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Answer: E

[math]{ }_{2.2} q_{[51]+0.5}=\frac{l_{[51]+0.5}-l_{53.7}}{l_{[51]+0.5}}[/math]

[math]l_{[51]+0.5}=0.5 l_{[51]}+0.5 l_{[51]+1}=0.5(97,000)+0.5(93,000)=95,000[/math]

[math]l_{53.7}=0.3 l_{53}+0.7 l_{54}=0.3(89,000)+0.7(83,000)=84,800[/math]

[math]{ }_{2.2} q_{[51]+0.5}=\frac{95,000-84,800}{95,000}=0.1074[/math]

[math]10,000_{2.2} q_{[51]+0.5}=1,074[/math]