For a fully discrete whole life insurance policy of 50,000 on (35), with premiums payable for a maximum of 10 years, you are given:

(i) Expenses of 100 are payable at the end of each year including the year of death

(ii) Mortality follows the Standard Ultimate Life Table

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

Calculate the annual gross premium using the equivalence principle.

• 790
• 800
• 810
• 820
• 830

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

Answer: D

By the equivalence principle, we have

[[math]] G \ddot{a}_{35: \overline{10}}=50,000 A_{35}+100 a_{35}+100 A_{35} [[/math]]

so

[math]G=\frac{50,100 A_{35}+100\left(\ddot{a}_{35}-1\right)}{\ddot{a}_{35: 10}}=\frac{50,100(0.09653)+100(17.9728)}{8.0926}=819.69[/math]

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