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

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

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]