Revision as of 22:10, 20 November 2023 by Admin (Created page with "'''Solution: A''' Let <math>h(i)=P V_A(i)-P V_L(i)</math>. Full immunization of a single liability requires both equations: <math display = "block"> \begin{aligned} & h(i)=0, h^{\prime}(i)=0 \\ & A_1 v+A_3 v^3-20,000 v^2=0 \\ & A_1 v^2+3 A_3 v^4-40,000 v^3=0 \\ & v=\frac{1}{1.055} \end{aligned} </math> Solve these two equations in two unknowns to get A<sub>1</sub> = 9478.67 {{soacopyright | 2023 }}")
Exercise
Nov 20'23
Answer
Solution: A
Let [math]h(i)=P V_A(i)-P V_L(i)[/math]. Full immunization of a single liability requires both equations:
[[math]]
\begin{aligned}
& h(i)=0, h^{\prime}(i)=0 \\
& A_1 v+A_3 v^3-20,000 v^2=0 \\
& A_1 v^2+3 A_3 v^4-40,000 v^3=0 \\
& v=\frac{1}{1.055}
\end{aligned}
[[/math]]
Solve these two equations in two unknowns to get A1 = 9478.67
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.