You are given the following information about Bond X and Bond Y:

i) Both bonds are 20-year bonds.

ii) Both bonds have face amount 1500.

iii) Both bonds have an annual nominal yield rate of 7% compounded semiannually.

iv) Bond X has an annual coupon rate of 10% paid semiannually and a redemption value C .

v) Bond Y has an annual coupon rate of 8% paid semiannually and a redemption value C+K

vi) The price of Bond X exceeds the price of Bond Y by 257.18.

Calculate K.

• 380−
• 88−
• 0
• 235
• 250

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: E

[[math]] \begin{array}{l}{{P_{x}=F r a_{\overline{40}|}+Cv^{40}=75a_{\overline{40}|}+Cv^{40}}}\\ {{P_{y}=P_{X}-257.18=60a_{\overline{40}|}+(C+K)v^{40}}}\\ {{P_{x}-P_{y}-257.18=15a_{\overline{40}|}-Kv^{40}}} \\ {{Kv^{40}=15a_{\overline{40}|}-257.18}}\\ {{K(0.2525772)=320.33-257.18}}\\ {{K=250.01}} \end{array} [[/math]]

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.