You are given the following extract from a table with a 3-year select period:

[math]x[/math]	[math]q_{[x]}[/math]	[math]q_{[x]+1}[/math]	[math]q_{[x]+2}[/math]	[math]q_{x+3}[/math]	[math]x+3[/math]
60	0.09	0.11	0.13	0.15	63
61	0.10	0.12	0.14	0.16	64
62	0.11	0.13	0.15	0.17	65
63	0.12	0.14	0.16	0.18	66
64	0.13	0.15	0.17	0.19	67

[math]e_{64}=5.10[/math]

Calculate [math]e_{[61]}[/math].

• 5.30
• 5.39
• 5.68
• 5.85
• 6.00

Answer: D

[math]e_{[61]}=e_{[61]: 37}+{ }_{3} p_{[61]}\left(e_{64}\right)[/math]

[math]p_{[61]}=0.90[/math],

[math]{ }_{2} p_{[61]}=0.9(0.88)=0.792[/math],

[math]{ }_{3} p_{[61]}=0.792(0.86)=0.68112[/math]

[math]e_{[61]: 3]}=\sum_{k=1}^{3}{ }_{k} p_{[61]}=0.9+0.792+0.68112=2.37312[/math]

[math]e_{[61]}=2.37312+0.68112 e_{64}=2.37312+0.68112(5.10)=5.847[/math]

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

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

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