For a fully discrete whole life insurance of 1000 on a select life [70], you are given:

(i) Ultimate mortality follows the Standard Ultimate Life Table

(ii) During the three-year select period, [math]q_{[x]+k}=(0.7+0.1 k) q_{x+k}, k=0,1,2[/math]

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

(iv) The net premium for this insurance is 35.168

Calculate [math]{ }_{1} V[/math], the net premium policy value at the end of year 1 for this insurance.

• 25.25
• 27.30
• 29.85
• 31.60
• 33.35

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

Answer: C

The simplest solution is recursive:

[math]{ }_{0} V=0[/math] since the policy values are net premium policy values.

[math]q_{[70]}=(0.7)(0.010413)=0.007289[/math]

[math]{ }_{1} V=\frac{(0+35.168)(1.05)-(1000)(0.007289)}{1-0.007289}=29.86[/math]

Prospectively, [math]q_{[70]+1}=(0.8)(0.011670)=0.009336 ; \quad q_{[70]+2}=(0.9)(0.013081)=0.011773[/math]

[[math]] \begin{aligned} & A_{[70]+1}=(0.009336) v+(1-0.009336)(0.011773) v^{2} \\ & \quad+(1-0.009336)(1-0.011773)(0.47580) v^{2}=0.44197 \\ & \ddot{a}_{[70]+1}=\left(1-A_{[70]+1}\right) / d=(1-0.44197) /(0.05 / 1.05)=11.7186 \\ & { }_{1} V=(1000)(0.44197)-(11.7186)(35.168)=29.85 \end{aligned} [[/math]]

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