For a fully discrete whole life insurance policy of 100,000 on (35), you are given:

(i) First year commissions are [math]19 \%[/math] of the annual gross premium

(ii) Renewal year commissions are [math]4 \%[/math] of the annual gross premium

(iii) Mortality follows the Standard Ultimate Life Table

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

Calculate the annual gross premium for this policy using the equivalence principle.

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

Answer: D

Let [math]G[/math] be the annual gross premium. By the equivalence principle, we have [math]G \ddot{a}_{35}=100,000 A_{35}+0.15 G+0.04 G \ddot{a}_{35}[/math]

so that

[[math]] G=\frac{100,000 A_{35}}{0.96 \ddot{a}_{35}-0.15}=\frac{100,000(0.09653)}{0.96(18.9728)-0.15}=534.38 [[/math]]

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