An insurer issues a fully discrete 20 -year endowment insurance policy of 1,000,000 on (35).

You are given:

i) First year expenses are 55% of the premium plus 150

ii) After the first year, expenses are 5% of the premium plus 50

iii) Mortality follows the Standard Ultimate Life Table

iv) [math]i=0.05[/math]

v) Premiums are determined using the equivalence principle

Calculate the annual gross premium on this policy.

• 29,000
• 30,000
• 31,000
• 32,000
• 33,000

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

Answer: D

[[math]] \begin{aligned} & A_{35: 20}=0.37981 \\ & \ddot{a}_{35: \overline{20}}=13.0240 \end{aligned} [[/math]]

APV of Premium [math]=[/math] APV of Benefits + APV of Expenses

APV of Benefits + APV of Expenses = [math]1,000,000 \times A_{35: \overline{20}}+50 \times \ddot{a}_{35: \overline{20}}+100=380,561.20[/math]

APV of Premium - APV of % Expenses [math]=(0.95) \times P \times \ddot{a}_{35: 20 \mid}-(0.5) \times P=11.8728 \times P \implies P=\frac{380,561.20}{11.8728}=32,053.20[/math]

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