Aakash has a liability of 6000 due in four years. This liability will be met with payments of A in two years and B in six years. Aakash is employing a full immunization strategy using an annual effective interest rate of 5%.

Calculate [math]|A-B|[/math].

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

Solution: D

Set up the following two equations in the two unknowns:

[[math]] \begin{array}{cc}{{A(1.05)^{2}+B(1.05)^{-2}=6000}}\\ {{2A(1.05)^{1}-2B(1.05)^{-3}=0.}}\end{array} [[/math]]

Solving simultaneously gives:

[[math]] \begin{array}{l}{{A=2721.09}}\\ {{B=3307.50}}\\ {{|A-B|=586.41}}\end{array} [[/math]]

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