For a fully discrete 3 -year endowment insurance of 1000 on [math](x)[/math], you are given:

(i) Expenses, payable at the beginning of the year, are:

Year(s)	Percent of Premium	Per Policy
1	20%	15
2 and 3	8%	5

(ii) The expense policy value at the end of year 2 is -23.64

(iii) The gross annual premium calculated using the equivalence principle is [math]G=368.05[/math]

(iv) [math]G=1000 P_{x: 3 \mid}+P^{e}[/math], where [math]P^{e}[/math] is the expense loading

Calculate [math]P_{x: 3 \mid}[/math].

• 0.290
• 0.295
• 0.300
• 0.305
• 0.310

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

Answer: E

Future expenses at [math]x+2=0.08 G+5[/math]

Expense load at [math]x+2=P^{e}[/math]

[math]-23.64=(0.08 G+5)-P^{e}[/math]

[math]\Rightarrow P^{e}=58.08[/math]

[math]1000 P_{x: 3 \mid}=368.05-58.08=309.97[/math]

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