For a fully discrete whole life insurance of 1000 on [math](x)[/math] with net premiums payable quarterly, you are given:

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

(ii) [math]\quad \ddot{a}_{x}=3.4611[/math]

(iii) [math]\quad P^{(W)}[/math] and [math]P^{(U D D)}[/math] are the annualized net premiums calculated using the 2-term Woolhouse [math](W)[/math] and the uniform distribution of deaths (UDD) assumptions, respectively

Calculate [math]\frac{P^{(U D D)}}{P^{(W)}}[/math].

• 1.000
• 1.002
• 1.004
• 1.006
• 1.008

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

Answer: B

Woolhouse: [math]\quad{ }^{W} \ddot{a}_{x}^{(4)}=3.4611-\frac{3}{8}=3.0861[/math]

[[math]] \begin{aligned} & { }^{U D D} \ddot{a}_{x}^{(4)}=\alpha(4) \ddot{a}_{x}-\beta(4) \\ & =1.00019(3.4611)-0.38272 \\ & =3.0790 \end{aligned} [[/math]]

and

[[math]] A_{x}=1-d \ddot{a}_{x}=1-(0.04762)(3.4611)=0.83518 [[/math]]

[math]P^{(W)}=\frac{1000(0.83518)}{3.0861}=270.63[/math]

[math]P^{(U D D)}=\frac{1000(0.83518)}{3.0790}=271.25[/math]

[math]\frac{P^{(U D D)}}{P^{(W)}}=\frac{271.25}{270.63}=1.0023[/math]

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