For a fully discrete 3 -year term insurance of 1000 on [math](x)[/math], you are given:

(i) [math]\quad p_{x}=0.975[/math]

(ii) [math]\quad i=0.06[/math]

(iii) The actuarial present value of the death benefit is 152.85

(iv) The annual net premium is 56.05

Calculate [math]p_{x+2}[/math].

• 0.88
• 0.89
• 0.90
• 0.91
• 0.92

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

Answer: D

[math]\ddot{a}_{x: 3}=\frac{\text { Actuarial PV of the benefit }}{\text { Level Annual Premium }}=\frac{152.85}{56.05}=2.727[/math]

[math]\ddot{a}_{x: 31}=1+\frac{0.975}{1.06}+\frac{0.975\left(p_{x+1}\right)}{(1.06)^{2}}=2.727[/math]

[math]\Rightarrow p_{x+1}=0.93[/math]

Actuarial PV of the benefit [math]=[/math]

[math]152.85=1,000\left[\frac{0.025}{1.06}+\frac{0.975(1-0.93)}{(1.06)^{2}}+\frac{0.975(0.93)\left(q_{x+2}\right)}{(1.06)^{3}}\right][/math]

[math]\Rightarrow q_{x+2}=0.09 \Rightarrow p_{x+2}=0.91[/math]

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