Revision as of 14:51, 20 November 2023 by Admin (Created page with "'''Solution: B''' Since the bond has no coupons, the Macaulay duration is the same as the amount of time until maturity, namely 4 years. Thus, the effective annual yield rate, y, is <math display = "block"> \left(\frac{1200}{1000} \right)^{1/4} -1 = 0.046635. </math> The modified duration equals the Macaulay duration divided by (1 + y). Thus the modified duration is 4/1.046635 = 3.82177 years. {{soacopyright | 2023 }}")
Exercise
Nov 20'23
Answer
Solution: B
Since the bond has no coupons, the Macaulay duration is the same as the amount of time until maturity, namely 4 years.
Thus, the effective annual yield rate, y, is
[[math]]
\left(\frac{1200}{1000} \right)^{1/4} -1 = 0.046635.
[[/math]]
The modified duration equals the Macaulay duration divided by (1 + y). Thus the modified duration is 4/1.046635 = 3.82177 years.
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.