Revision as of 22:35, 19 November 2023 by Admin (Created page with "'''Solution: A''' Let <math>i</math> be the yield rate, <math>\mathrm{v}=1 /(1+i)</math>, and let <math>n</math> be the term. For Bond A, 20,000v <math>v^n=10,000</math> and so <math>v^n=0.5</math>. For Bond <math>\mathrm{B}, 10,835 \cdot 58\left(v^n+0.04 a_{n i}\right)=10,000</math> and so <math display="block"> a_{n i}=\left(\frac{10,000}{10,835.58}-0.5\right) / 0.04=10.5721 \text {. } </math> For Bond C, <math display="block"> 10,000=X\left(v^n+0.03 a_{n i}\righ...")
Exercise
ABy Admin
Nov 19'23
Answer
Solution: A
Let [math]i[/math] be the yield rate, [math]\mathrm{v}=1 /(1+i)[/math], and let [math]n[/math] be the term. For Bond A, 20,000v [math]v^n=10,000[/math] and so [math]v^n=0.5[/math]. For Bond [math]\mathrm{B}, 10,835 \cdot 58\left(v^n+0.04 a_{n i}\right)=10,000[/math] and so
[[math]]
a_{n i}=\left(\frac{10,000}{10,835.58}-0.5\right) / 0.04=10.5721 \text {. }
[[/math]]
For Bond C,
[[math]]
10,000=X\left(v^n+0.03 a_{n i}\right)=0.81716 X \Rightarrow X=12,237.51
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.