(35) purchases a fully discrete whole life insurance policy of 100,000 .

You are given:

(i) The annual gross premium, calculated using the equivalence principle, is 1770

(ii) The expenses in policy year 1 are [math]50 \%[/math] of premium and 200 per policy

(iii) The expenses in policy years 2 and later are [math]10 \%[/math] of premium and 50 per policy

(iv) All expenses are incurred at the beginning of the policy year

(v) [math]\quad i=0.035[/math]

Calculate [math]\ddot{a}_{35}[/math].

• 20.0
• 20.5
• 21.0
• 21.5
• 22.0

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

Answer: B

Per equivalence Principle:

[[math]] \begin{aligned} G \ddot{a}_{35} & =100,000 A_{35}+0.4 G+150+0.1 G \ddot{a}_{35}+50 \ddot{a}_{35} \\ 1770 \ddot{a}_{35} & =100,000\left(1-d \ddot{a}_{35}\right)+0.4(1770)+150+0.1(1770) \ddot{a}_{35}+50 \ddot{a}_{35} \\ 1770 \ddot{a}_{35} & =100,000+708+150+\ddot{a}_{35}\left(177+50-100,000\left(\frac{0.035}{1.035}\right)\right) \end{aligned} [[/math]]

Solving for [math]\ddot{a}_{35}[/math], we have

[[math]] \ddot{a}=\frac{100,858}{1770+3154.64}=\frac{100,858}{4924.64}=20.48 [[/math]]

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