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Nov 20'23
Exercise
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].
- 0
- 146
- 293
- 586
- 881
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Nov 20'23
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.