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Jan 18'24
Exercise
For a whole life insurance of 1000 on (50), you are given:
(i) The death benefit is payable at the end of the year of death
(ii) Mortality follows the Standard Ultimate Life Table
(iii) [math]i=0.04[/math] in the first year, and [math]i=0.05[/math] in subsequent years
Calculate the actuarial present value of this insurance.
- 187
- 189
- 191
- 193
- 195
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Jan 18'24
Answer: C
Let [math]A_{51}^{\text {SULT }}[/math] designate [math]A_{51}[/math] using the Standard Ultimate Life Table at [math]5 \%[/math].
[[math]]
\begin{aligned}
\mathrm{APV}(\text { insurance }) & =1000\left(\frac{1}{1.04}\right)\left(q_{50}+p_{50} A_{51}^{S U L T}\right) \\
& =1000\left(\frac{1}{1.04}\right)[0.001209+(1-0.001209)(0.19780)] \\
& =191.12
\end{aligned}
[[/math]]
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.