For a fully discrete 10 -year deferred whole life annuity-due of 1000 per month on (55), you are given:

(i) The premium, [math]G[/math], will be paid annually at the beginning of each year during the deferral period

(ii) Expenses are expected to be 300 per year for all years, payable at the beginning of the year

(iii) Mortality follows the Standard Ultimate Life Table

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

(v) Using the two-term Woolhouse approximation, the expected loss at issue is -800 Calculate [math]G[/math].

• 12,110
• 12,220
• 12,330
• 12,440
• 12,550

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

Answer: C

Need [math]\operatorname{EPV}([/math] Ben [math]+\operatorname{Exp})-\operatorname{EPV}([/math] Prem [math])=-800[/math]

[math]\operatorname{EPV}([/math] Prem [math])=G \ddot{a}_{55: 10}=8.0192 G[/math]

[[math]] \begin{aligned} \operatorname{EPV}(\operatorname{Ben}+\operatorname{Exp}) & =12,000{ }_{10} \ddot{a}_{55}^{(12)}+300 \ddot{a}_{55} \\ & =12,000_{10} E_{55} \ddot{a}_{65}^{(12)}+300 \ddot{a}_{55} \\ & =12,000_{10} E_{55}\left(\ddot{a}_{65}-\frac{m-1}{2 m}\right)+300 \ddot{a}_{55} \\ & =12,000(0.59342)(13.5498-11 / 24)+300(16.0599) \\ & =98,042.83 \end{aligned} [[/math]]

Therefore, [math]\quad 98,042.83-8.0192 G=-800[/math]

[[math]] G=12,326 [[/math]]

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