Revision as of 01:55, 20 January 2024 by Admin (Created page with "An insurer issues a 30-year term insurance policy on (40). You are given: i) Net premiums of 750 are payable quarterly ii) The death benefit, payable at the end of the quarter of death, is <math>1,000,000</math> iii) <math>{ }_{t} V</math> denotes the net premium policy value at time <math>t, t \geq 0</math> iv) <math>10.5^{V}=10,000</math> v) <math>q_{50}=0.01</math> vi) Mortality is uniformly distributed over each year of age vii) <math>i=0.05</math> Calculate <...")
ABy Admin
Jan 20'24
Exercise
An insurer issues a 30-year term insurance policy on (40). You are given:
i) Net premiums of 750 are payable quarterly
ii) The death benefit, payable at the end of the quarter of death, is [math]1,000,000[/math]
iii) [math]{ }_{t} V[/math] denotes the net premium policy value at time [math]t, t \geq 0[/math]
iv) [math]10.5^{V}=10,000[/math] v) [math]q_{50}=0.01[/math]
vi) Mortality is uniformly distributed over each year of age
vii) [math]i=0.05[/math]
Calculate [math]{ }_{10.75} V[/math].
- 8,360
- 8,370
- 8,380
- 8,390
- 8,400
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Jan 20'24
Answer: D
[[math]]
\begin{aligned}
& \left({ }_{10.5} V+P\right)(1+i)^{0.25}=1,000,000 \times{ }_{0.25} q_{50.5}+{ }_{0.25} p_{50.5} \times{ }_{50.75} V \\
& (10,000+750)(1+0.05)^{0.25}=1,000,000 \times\left(1-\frac{(1-0.75 \times 0.01)}{(1-0.5 \times 0.01)}\right)+\left(\frac{(1-0.75 \times 0.01)}{(1-0.5 \times 0.01)}\right) \times{ }_{50.75} V \\
& { }_{50.75} V=8,390
\end{aligned}
[[/math]]
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.