For a fully discrete whole life insurance policy of [math]1,000,000[/math] on (50), you are given:

(i) The annual gross premium, calculated using the equivalence principle, is 11,800

(ii) Mortality follows the Standard Ultimate Life Table

(iii) [math]\quad i=0.05[/math]

Calculate the expense loading, [math]P^{e}[/math], for this policy.

• 480
• 580
• 680
• 780
• 880

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

Answer: C

[math]P^{g}=P^{n}+P^{e} \quad[/math] where [math]P^{e}[/math] is the expense loading

[math]P^{n}=1,000,000 \frac{A_{50}}{\ddot{a}_{50}}=1,000,000\left(\frac{0.18931}{17.0245}\right)=11,119.86[/math]

[math]P^{e}=P^{g}-P^{n}=11,800-11,120=680[/math]

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