For a fully discrete whole life insurance of 100,000 on (40) you are given:

(i) Expenses incurred at the beginning of the first year are 300 plus [math]50 \%[/math] of the first year premium

(ii) Renewal expenses, incurred at the beginning of the year, are [math]10 \%[/math] of each of the renewal premiums

(iii) Mortality follows the Standard Ultimate Life Table

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

(v) Gross premiums are calculated using the equivalence principle

Calculate the gross premium policy value for this insurance immediately after the second premium and associated renewal expenses are paid.

• 200
• 340
• 560
• 720
• 1060

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

Answer: D

Let [math]G[/math] be the annual gross premium.

Using the equivalence principle, [math]0.90 G \ddot{a}_{40}-0.40 G=100,000 A_{40}+300[/math]

So [math]G=\frac{100,000(0.12106)+300}{0.90(18.4578)-0.40}=765.2347[/math]

The gross premium policy value after the first year and immediately after the second premium and associated expenses are paid is

[[math]] \begin{aligned} & 100,000 A_{41}-0.90 G\left(\ddot{a}_{41}-1\right) \\ & =12,665-0.90(765.2347)(17.3403) \\ & =723 \end{aligned} [[/math]]

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