Revision as of 13:49, 20 November 2023 by Admin (Created page with "'''Solution: E''' Let x be the annual payment amount. Macaulay duration is <math display = "block"> \frac{\frac{1 x}{1.1}+\frac{2 x}{1.1^2}+\frac{3 x}{1.1^3}+\cdots+\frac{7 x}{1.1^7}}{\frac{x}{1.1}+\frac{x}{1.1^2}+\frac{x}{1.1^3}+\cdots+\frac{x}{1.1^7}} =\frac{17.6315}{4.8684} = 3.62 </math> Alternatively, the duration can be calculated as <math display = "block">\frac{(Ia)_{\overline{7}|0.01}}{a_{\overline{7}|0.01}}</math> {{soacopyright | 2023 }}")
Exercise
Nov 20'23
Answer
Solution: E
Let x be the annual payment amount. Macaulay duration is
[[math]]
\frac{\frac{1 x}{1.1}+\frac{2 x}{1.1^2}+\frac{3 x}{1.1^3}+\cdots+\frac{7 x}{1.1^7}}{\frac{x}{1.1}+\frac{x}{1.1^2}+\frac{x}{1.1^3}+\cdots+\frac{x}{1.1^7}}
=\frac{17.6315}{4.8684} = 3.62
[[/math]]
Alternatively, the duration can be calculated as
[[math]]\frac{(Ia)_{\overline{7}|0.01}}{a_{\overline{7}|0.01}}[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.