Revision as of 14:58, 20 November 2023 by Admin (Created page with "'''Solution: B''' <math display = "block"> \begin{aligned} & P_L=1000(1+i)^{-2}+300(1+i)^{-4} \\ & P_L=1153.84 \\ & P_L^{\prime}=-2000(1+i)^{-3}-1200(1+i)^{-5} \\ & P_L^{\prime}=-2667.91 \\ & P_A=X(1+i)^{-1}+Y(1+i)^{-3} \\ & 1153.84=0.95238 X+0.86384 Y \\ & P_L^{\prime}=-X(1+i)^{-2}-3 Y(1+i)^{-4} \\ & -2667.91=-0.90703 X-2.46811 Y \end{aligned} </math> So, we have two equations and two unknowns. Solving simultaneously, we get: <math display = "block"> Y=953.57, \quad X...")
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Exercise

AAdmin
Nov 20'23

Answer

Solution: B

[[math]] \begin{aligned} & P_L=1000(1+i)^{-2}+300(1+i)^{-4} \\ & P_L=1153.84 \\ & P_L^{\prime}=-2000(1+i)^{-3}-1200(1+i)^{-5} \\ & P_L^{\prime}=-2667.91 \\ & P_A=X(1+i)^{-1}+Y(1+i)^{-3} \\ & 1153.84=0.95238 X+0.86384 Y \\ & P_L^{\prime}=-X(1+i)^{-2}-3 Y(1+i)^{-4} \\ & -2667.91=-0.90703 X-2.46811 Y \end{aligned} [[/math]]

So, we have two equations and two unknowns. Solving simultaneously, we get:

[[math]] Y=953.57, \quad X=346.61, \quad \frac{Y}{X}=2.75 [[/math]]

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

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