Revision as of 19:13, 19 November 2023 by Admin (Created page with "'''Solution: D''' Let F be the face amount of Bond X. Then, <math display = "block"> 2695.39=200a_{\overline{15}|}+F_{V}^{15}\mathrm{~and~3490.78}=200a_{\overline{15}|}+F_{V}^{15}. </math> Subtract the first equation from the second to obtain <math>795.39 = Fv^{15}.</math> Then for bond X, <math display = "block"> 2695.39=200a_{\overline{15}|}+795.39\Rightarrow a_{\overline{15}|}=(2695.39-795.39)/200=9.5. </math> This implies <math>i =0.0634</math>. Then <math...")
Exercise
ABy Admin
Nov 19'23
Answer
Solution: D
Let F be the face amount of Bond X. Then,
[[math]]
2695.39=200a_{\overline{15}|}+F_{V}^{15}\mathrm{~and~3490.78}=200a_{\overline{15}|}+F_{V}^{15}.
[[/math]]
Subtract the first equation from the second to obtain [math]795.39 = Fv^{15}.[/math] Then for bond X,
[[math]]
2695.39=200a_{\overline{15}|}+795.39\Rightarrow a_{\overline{15}|}=(2695.39-795.39)/200=9.5.
[[/math]]
This implies [math]i =0.0634[/math]. Then
[[math]]
9.5=(1- v^{15})/0.0634\Longrightarrow v^{15}=1-0.0634(9.5)=0.3977
[[/math]]
and [math]F = 795.39 / 0.3977 = 2000[/math]. The coupon rate is 200/2000 = 10.0%.
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.