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ABy Admin
Jan 19'24
Exercise
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.
ABy Admin
Jan 19'24
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.