Revision as of 20:35, 19 January 2024 by Admin (Created page with "'''Answer: D''' <math>\ddot{a}_{x: 3}=\frac{\text { Actuarial PV of the benefit }}{\text { Level Annual Premium }}=\frac{152.85}{56.05}=2.727</math> <math>\ddot{a}_{x: 31}=1+\frac{0.975}{1.06}+\frac{0.975\left(p_{x+1}\right)}{(1.06)^{2}}=2.727</math> <math>\Rightarrow p_{x+1}=0.93</math> Actuarial PV of the benefit <math>=</math> <math>152.85=1,000\left[\frac{0.025}{1.06}+\frac{0.975(1-0.93)}{(1.06)^{2}}+\frac{0.975(0.93)\left(q_{x+2}\right)}{(1.06)^{3}}\right]</mat...")
Exercise
ABy Admin
Jan 19'24
Answer
Answer: D
[math]\ddot{a}_{x: 3}=\frac{\text { Actuarial PV of the benefit }}{\text { Level Annual Premium }}=\frac{152.85}{56.05}=2.727[/math]
[math]\ddot{a}_{x: 31}=1+\frac{0.975}{1.06}+\frac{0.975\left(p_{x+1}\right)}{(1.06)^{2}}=2.727[/math]
[math]\Rightarrow p_{x+1}=0.93[/math]
Actuarial PV of the benefit [math]=[/math]
[math]152.85=1,000\left[\frac{0.025}{1.06}+\frac{0.975(1-0.93)}{(1.06)^{2}}+\frac{0.975(0.93)\left(q_{x+2}\right)}{(1.06)^{3}}\right][/math]
[math]\Rightarrow q_{x+2}=0.09 \Rightarrow p_{x+2}=0.91[/math]
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