Revision as of 01:37, 19 January 2024 by Admin (Created page with "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. <ul class="mw-excansopts"><li> 162,000<li> 164,000<li> 165,200<li> 166,400<li> 168,800</ul> {{soa...")
ABy Admin
Jan 19'24
Exercise
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.
ABy Admin
Jan 19'24
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.