Revision as of 12:36, 20 November 2023 by Admin (Created page with "'''Solution: B''' The Macaulay duration of the perpetuity is <math display = "block"> \frac{\sum_{n=1}^{\infty}n\nu^{n}}{\sum_{n=1}^{\infty}\nu^{n}}=\frac{(Ia)_{\overline{\infty}|}}{a_{\overline{\infty}|}}=\frac{\left(1+i\right)/i^{2}}{i}=\frac{1+i}{i}=1+1/i=17.6. </math> This implies that i = 1/16.6. With i = 2i = 2/16.6, the duration is 1 + 16.6/2 = 9.3. {{soacopyright | 2023 }}")
Exercise
Nov 20'23
Answer
Solution: B
The Macaulay duration of the perpetuity is
[[math]]
\frac{\sum_{n=1}^{\infty}n\nu^{n}}{\sum_{n=1}^{\infty}\nu^{n}}=\frac{(Ia)_{\overline{\infty}|}}{a_{\overline{\infty}|}}=\frac{\left(1+i\right)/i^{2}}{i}=\frac{1+i}{i}=1+1/i=17.6.
[[/math]]
This implies that i = 1/16.6. With i = 2i = 2/16.6, the duration is 1 + 16.6/2 = 9.3.
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.