excans:A8f381140d: Difference between revisions
(Created page with "'''Answer: D''' The equation of value is given by Actuarial Present Value of Premiums = Actuarial Present Value of Death Benefits. The death benefit in the first year is <math>1000+P</math>. The death benefit in the second year is <math>1000+2 P</math>. The formula is <math>P \ddot{a}_{80: 2}=1000 A_{80: 2}^{1}+P(I A)_{80: 2}^{1}</math>. Solving for <math>\mathrm{P}</math> we obtain <math>P=\frac{1000 A_{80: 21}^{1}}{\ddot{a}_{80: 21}-(I A)_{80: 21}^{1}}</math>. <m...") |
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<math>P=\frac{65.08552}{1.93917-0.09846}=35.36 \rightarrow D</math> | <math>P=\frac{65.08552}{1.93917-0.09846}=35.36 \rightarrow D</math> | ||
{{soacopyright|2024}} | |||
Latest revision as of 19:55, 19 January 2024
Answer: D
The equation of value is given by
Actuarial Present Value of Premiums = Actuarial Present Value of Death Benefits.
The death benefit in the first year is [math]1000+P[/math]. The death benefit in the second year is [math]1000+2 P[/math].
The formula is [math]P \ddot{a}_{80: 2}=1000 A_{80: 2}^{1}+P(I A)_{80: 2}^{1}[/math].
Solving for [math]\mathrm{P}[/math] we obtain [math]P=\frac{1000 A_{80: 21}^{1}}{\ddot{a}_{80: 21}-(I A)_{80: 21}^{1}}[/math].
[math]\ddot{a}_{80: 21}=1+p_{80} v=1+\frac{0.967342}{1.03}=1.93917[/math]
[math]1000 A_{80: 21}^{1}=1000\left(v q_{80}+v^{2} p_{80} q_{81}\right)=1000\left(\frac{0.032658}{1.03}+\frac{(0.967342)(0.036607)}{1.03^{2}}\right)=65.08552[/math]
[math](I A)_{80: 21}^{1}=v q_{80}+2 v^{2} p_{80} q_{81}=\frac{0.032658}{1.03}+(2) \frac{(0.967342)(0.036607)}{1.03^{2}}=0.09846[/math]
[math]P=\frac{65.08552}{1.93917-0.09846}=35.36 \rightarrow D[/math]
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.