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].

• 200
• 213
• 226
• 239
• 252

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.