For a fully discrete 10 -year term life insurance policy on [math](x)[/math], you are given:

(i) Death benefits are 100,000 plus the return of all gross premiums paid without interest

(ii) Expenses are [math]50 \%[/math] of the first year's gross premium, [math]5 \%[/math] of renewal gross premiums and 200 per policy expenses each year

(iii) Expenses are payable at the beginning of the year

(iv) [math]A_{x: 10}^{1}=0.17094[/math]

(v) [math]\quad(I A)_{x: 10 \mid}^{1}=0.96728[/math]

(vi) [math]\quad \ddot{a}_{x: 100}=6.8865[/math]

Calculate the gross premium using the equivalence principle.

• 3200
• 3300
• 3400
• 3500
• 3600

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

Answer: E

[[math]] \begin{aligned} & G \ddot{a}_{x: \overline{10}}=100,000 A_{x: 10 \mid}^{1}+G(I A)_{x: 10 \mid}^{1}+0.45 G+0.05 G \ddot{a}_{x: 10 \mid}+200 \ddot{a}_{x: \overline{10}} \\ & G=\frac{(100,000)(0.17094)+200(6.8865)}{(1-0.05)(6.8865)-0.96728-0.45}=3604.23 \end{aligned} [[/math]]

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