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| rev | 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 }}") | Nov 20'23 at 22:10 | +405 |