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.

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.