For a whole life insurance of 100,000 on (45) with premiums payable monthly for a period of 20 years, you are given:

(i) The death benefit is paid immediately upon death

(ii) Mortality follows the Standard Ultimate Life Table

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

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

Calculate the monthly net premium.

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

Answer: C

Let the monthly net premium [math]=\pi[/math]

[[math]] \begin{aligned} & 12 \pi=\frac{100,000 \bar{A}_{45}}{\ddot{a}_{45: 20}^{(12)}} \\ & \alpha(12)=1.00020 \\ & \beta(12)=0.46651 \\ & \frac{i}{\delta}=1.02480 \\ & 100,000 \bar{A}_{45}=100,000 \frac{i}{\delta} A_{45}=(1.02480)(15,161)=15,536.99 \\ & \ddot{a}_{45: 20}^{(12)}=\alpha(12) \ddot{a}_{45: 20}-\beta(12)\left(1-{ }_{20} E_{45}\right) \\ & =1.00020[12.9391]-0.46651(1-0.35994) \\ & =12.6431 \\ & 12 \pi=\frac{15,536.99}{12.6431} \\ & 12 \pi=1228.891 \\ & \pi=102.41 \end{aligned} [[/math]]

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