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].
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.