You are given:

(i) Mortality follows the Standard Ultimate Life Table

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

(iii) [math]\quad i=0.05[/math]

Calculate [math]\frac{d}{dt}(\overline{I}\overline{a})_{40:\overline{t}|}[/math] at [math]t=10.5[/math].

• 5.8
• 6.0
• 6.2
• 6.4
• 6.6

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

Answer: C

[math](\bar{I} \bar{a})_{40: t}=\int_{0}^{t} s_{s} p_{40} v^{s} d s \Rightarrow \frac{d(\overline{I \bar{a}})_{40: \nexists}}{d t}=t_{t} p_{40} v^{t}[/math]

At [math]t=10.5[/math],

[math]10.5_{10.5} E_{40}=10.5_{10} p_{400.5} p_{50} v^{10.5}[/math]

[math]=10.5_{10} E_{400.5} p_{50} v^{0.5}[/math]

[math]=10.5 \times 0.60920 \times(1-0.5 \times 0.001209)(0.975900073)[/math]

[math]=6.239[/math]

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