For a fully discrete whole life insurance of 100 on [math](x)[/math], you are given:

(i) [math]\quad q_{x+15}=0.10[/math]

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

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

(iv) [math]{ }_{t} V[/math] denotes the net premium policy value at time [math]t[/math]

(v) [math]{ }_{16} V=49.78[/math]

Calculate [math]{ }_{15.6} \mathrm{~V}[/math].

• 49.7
• 50.0
• 50.3
• 50.6
• 50.9

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

Answer: E

[[math]] \begin{aligned} & { }_{15.6} V(1+i)^{0.4}={ }_{0.4} p_{x+15.6} \quad{ }_{16} V+{ }_{0.4} q_{x+15.6} 100 \\ & { }_{15.6} V(1.05)^{0.4}=0.957447(49.78)+0.042553(100) \\ & { }_{15.6} V=50.91 \end{aligned} [[/math]]

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