For a fully discrete whole life insurance policy on (61), you are given:

(i) The annual gross premium using the equivalence principle is 500

(ii) Initial expenses, incurred at policy issue, are [math]15 \%[/math] of the premium

(iii) Renewal expenses, incurred at the beginning of each year after the first, are [math]3 \%[/math] of the premium

(iv) Mortality follows the Standard Ultimate Life Table

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

Calculate the amount of the death benefit.

• 23,300
• 23,400
• 23,500
• 23,600
• 23,700

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

Answer: A

Let [math]B[/math] be the amount of death benefit.

[math]\mathrm{EPV}([/math] Premiums [math])=500 \ddot{a}_{61}=500(14.6491)=7324.55[/math]

[math]\mathrm{EPV}([/math] Benefits [math])=\mathrm{B} \cdot A_{61}=(0.30243) \mathrm{B}[/math]

[math]\operatorname{EPV}([/math] Expenses [math])=(0.12)(500)+(0.03)(500) \ddot{a}_{61}=(0.12)(500)+(0.03)(7324.55)=279.74[/math]

[math]\mathrm{EPV}([/math] Premiums [math])=\mathrm{EPV}([/math] Benefits [math])+\mathrm{EPV}([/math] Expenses [math])[/math]

[math]7324.55=(0.30243) \mathrm{B}+279.74[/math]

[math]7044.81=(0.30243) \mathrm{B}[/math]

[math]\mathrm{B}=23,294[/math]

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