Revision as of 22:38, 20 November 2023 by Admin (Created page with "'''Solution: B''' Use the full immunization equations and let <math>N</math> be the maturity value of the asset maturing in <math>n</math> years. <math display="block"> \begin{aligned} & 242,180(1.07)^7+N(1.07)^{-(n-12)}-1,750,000=0 \\ & 242,180(7)(1.07)^7-N(n-12)(1.07)^{-(n-12)}=0 \end{aligned} </math> From the first equation: <math display="block"> N(1.07)^{-(n-12)}=1,750,000-242,180(1.07)^7=1,361,112 \text {. } </math> Substituting this in the second equation:...")
Exercise
Nov 20'23
Answer
Solution: B
Use the full immunization equations and let [math]N[/math] be the maturity value of the asset maturing in [math]n[/math] years.
[[math]]
\begin{aligned}
& 242,180(1.07)^7+N(1.07)^{-(n-12)}-1,750,000=0 \\
& 242,180(7)(1.07)^7-N(n-12)(1.07)^{-(n-12)}=0
\end{aligned}
[[/math]]
From the first equation:
[[math]]
N(1.07)^{-(n-12)}=1,750,000-242,180(1.07)^7=1,361,112 \text {. }
[[/math]]
Substituting this in the second equation: [math]n-12=242,180(7)(1.07)^7 / 1,361,112=2[/math] and so [math]n=14[/math]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.