For a 20 -year deferred whole life annuity-due with annual payments of 30,000 on (40), you are given:

(i) The single net premium is refunded without interest at the end of the year of death if death occurs during the deferral period

(ii) Mortality follows the Standard Ultimate Life Table

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

Calculate the single net premium for this annuity.

• 162,000
• 164,000
• 165,200
• 166,400
• 168,800

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

Answer: D

[[math]] \begin{aligned} P & =30,000_{20} \ddot{a}_{40}+P A_{40: 20}^{1} \\ \Rightarrow \quad P & =30,000_{20} \ddot{a}_{40} /\left(1-A_{40: 20}^{1}\right) \\ & =30,000(5.46429) /(1-0.0146346)=166,363 \end{aligned} [[/math]]

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