For a fully continuous whole life insurance policy of 100,000 on (35), you are given:

(i) The density function of the future lifetime of a newborn:

[[math]] f(t)= \begin{cases}0.01 e^{-0.01 t}, & 0 \leq t\lt70 \\ g(t), & t \geq 70\end{cases} [[/math]]

(ii) [math]\delta=0.05[/math]

(iii) [math]\quad \bar{A}_{70}=0.51791[/math]

Calculate the annual net premium rate for this policy.

• 1000
• 1110
• 1220
• 1330
• 1440

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

Answer: D

[math]\bar{A}_{35}=\left(1-e^{-35(\mu+\delta)}\right) \times\left(\frac{\mu}{\mu+\delta}\right)+e^{-35(\mu+\delta)} \bar{A}_{70}=0.063421+0.146257=0.209679[/math]

[math]\bar{a}_{35}=\frac{1-\bar{A}_{35}}{\delta}=\frac{1-0.209679}{0.05}=15.80642[/math]

[math]\bar{P}_{35}=\frac{\bar{A}_{35}}{\bar{a}_{35}}=\frac{0.209679}{15.80642}=0.0132654[/math]

The annual net premium for this policy is therefore [math]100,000 \times 0.0132654=1,326.54[/math]

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