Revision as of 02:02, 19 January 2024 by Admin (Created page with "For a special fully discrete 2 -year term insurance on <math>(x)</math>, you are given: (i) <math>q_{x}=0.01</math> (ii) <math>\quad q_{x+1}=0.02</math> (iii) <math>\quad i=0.05</math> (iv) The death benefit in the first year is 100,000 (v) Both the benefits and premiums increase by <math>1 \%</math> in the second year Calculate the annual net premium in the first year. <ul class="mw-excansopts"><li> 1410</li><li> 1417<li> 1424<li> 1431<li> 1438</ul> {{soacopyrigh...")
ABy Admin
Jan 19'24
Exercise
For a special fully discrete 2 -year term insurance on [math](x)[/math], you are given:
(i) [math]q_{x}=0.01[/math]
(ii) [math]\quad q_{x+1}=0.02[/math]
(iii) [math]\quad i=0.05[/math]
(iv) The death benefit in the first year is 100,000
(v) Both the benefits and premiums increase by [math]1 \%[/math] in the second year Calculate the annual net premium in the first year.
- 1410
- 1417
- 1424
- 1431
- 1438
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Jan 19'24
Answer: B
Let [math]P[/math] be the net premium for year 1 .
Then:
[[math]]
\begin{aligned}
& P+1.01 P v p_{x}=100,000 v q_{x}+(1.01)(100,000) v^{2} p_{x} q_{x+1} \\
& P\left[1+\frac{1.01}{1.05} 0.99\right]=100,000\left(\frac{0.01}{1.05}+\frac{(1.01)(0.99)(0.02)}{(1.05)^{2}}\right) \Rightarrow P=1416.93
\end{aligned}
[[/math]]
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.