The gross annual premium, [math]G[/math], for a fully discrete 5 -year endowment insurance of 1000 issued on [math](x)[/math] is calculated using the equivalence principle. You are given:
(i) [math]\quad 1000 P_{x: 5 \mid}=187.00[/math]
(ii) The expense policy value at the end of the first year, [math]{ }_{1} V^{e}=-38.70[/math]
(iii) [math]q_{x}=0.008[/math]
(iv) Expenses, payable at the beginning of the year, are:
| Year | Percent of Premium | Per Policy |
|---|---|---|
| First | 25% | 10 |
| Renewal | 5% | 5 |
(v) [math]\quad i=0.03[/math]
Calculate [math]G[/math].
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Answer: B
Since [math]G[/math] is determined using the equivalence principle, [math]{ }_{0} V=0[/math]
Then, [math]{ }_{1} V^{e}=\frac{(0+\overbrace{G-187}^{P^{e}}-0.25 G-10)(1.03)}{0.992}=-38.7[/math]
[math]\Rightarrow 0.75 G=\frac{-38.7(0.992)}{1.03}+187+10=159.72[/math]
[math]\Rightarrow G=212.97[/math]
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.