Revision as of 01:37, 20 January 2024 by Admin (Created page with "For a fully discrete whole life insurance policy of 100,000 on [55], a professional skydiver, you are given: (i) Level premiums are paid annually (ii) Mortality follows a 2-year select and ultimate table (iii) <math>\quad i=0.04</math> (iv) The following table of values for <math>A_{[x]+t}</math> : {| class="table table-bordered" ! <math>x</math> !! <math>A_{[x]}</math> !! <math>A_{[x]+1}</math> !! <math>A_{x+2}</math> |- | 55 || 0.23 || 0.24 || 0.25 |- | 56 || 0.25...")
ABy Admin
Jan 20'24
Exercise
For a fully discrete whole life insurance policy of 100,000 on [55], a professional skydiver, you are given:
(i) Level premiums are paid annually
(ii) Mortality follows a 2-year select and ultimate table
(iii) [math]\quad i=0.04[/math]
(iv) The following table of values for [math]A_{[x]+t}[/math] :
| [math]x[/math] | [math]A_{[x]}[/math] | [math]A_{[x]+1}[/math] | [math]A_{x+2}[/math] |
|---|---|---|---|
| 55 | 0.23 | 0.24 | 0.25 |
| 56 | 0.25 | 0.26 | 0.27 |
| 57 | 0.27 | 0.28 | 0.29 |
| 58 | 0.29 | 0.30 | 0.31 |
Calculate the Full Preliminary Term reserve at time 3.
- 2700
- 3950
- 5200
- 6450
- 7800
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Jan 20'24
Answer: B
[[math]]
\begin{aligned}
& { }_{3} V^{F P T}=100,000 A_{[55]+3}-100,000 P_{[55]+1} \ddot{a}_{[55]+3} \\
& =100,000 A_{58}-100,000 \frac{A_{[55]+1}}{\ddot{a}_{[55]+1}} \ddot{a}_{58} \\
& =100,000\left(0.27-\frac{0.24}{\frac{1-0.24}{d}} \cdot \frac{1-0.27}{d}\right) \\
&= 3947.37
\end{aligned}
[[/math]]
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.