For a whole life insurance of 100,000 on [math](x)[/math], you are given:

(i) Death benefits are payable at the moment of death

(ii) Deaths are uniformly distributed over each year of age

(iii) Premiums are payable monthly

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

(v) [math]\quad \ddot{a}_{x}=9.19[/math]

Calculate the monthly net premium.

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

Answer: C

Assuming UDD

Let [math]P=[/math] monthly net premium

[math]\mathrm{EPV}([/math] premiums [math])=12 P \ddot{a}_{x}^{(12)} \cong 12 P\left[\alpha(12) \dot{a}_{x}-\beta(12)\right][/math]

[[math]] \begin{aligned} & =12 P[1.00020(9.19)-0.46651] \\ & =104.7039 P \end{aligned} [[/math]]

[math]\mathrm{EPV}([/math] benefits [math])=100,000 \bar{A}_{x}[/math]

[[math]] \begin{aligned} & =100,000 \frac{i}{\delta} A_{x}=100,000 \frac{i}{\delta}\left(1-d \ddot{a}_{x}\right) \\ & =100,000 \frac{0.05}{\ln (1.05)}\left(1-\frac{0.05}{1.05}(9.19)\right) \\ & =57,632.62 \end{aligned} [[/math]]

[math]P=\frac{57,632.62}{104.7039}=550.43[/math]

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