exercise:F52f6003cc

Jan 20'24

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.

Jan 20'24

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]]