Revision as of 18:18, 19 November 2023 by Admin (Created page with "'''Solution: D''' Throughout the solution, let <math>j=i/2</math>. For bond A, the coupon rate is <math>(i+0.04)/2=j+0.02.</math> For bond B, the coupon rate is <math>(i-0.04)/2=j-0.02. </math> The price of bond A is <math>P_{A}=10,000(j+0.02)a_{\overline{30}|j}+10,000(1+j)^{-20}. </math> The price of bond B is <math>P_{B}=10,000(j-0.02)a_{\overline{20}|i}+10,000(1+j)^{-20} </math> Thus, <math display = "block"> \begin{align*} P_{A}-P_{B}=5,341.12=[200-(-200)]a_{\...")
Exercise
ABy Admin
Nov 19'23
Answer
Solution: D
Throughout the solution, let [math]j=i/2[/math].
For bond A, the coupon rate is [math](i+0.04)/2=j+0.02.[/math]
For bond B, the coupon rate is [math](i-0.04)/2=j-0.02. [/math]
The price of bond A is [math]P_{A}=10,000(j+0.02)a_{\overline{30}|j}+10,000(1+j)^{-20}. [/math]
The price of bond B is [math]P_{B}=10,000(j-0.02)a_{\overline{20}|i}+10,000(1+j)^{-20} [/math]
Thus,
[[math]]
\begin{align*}
P_{A}-P_{B}=5,341.12=[200-(-200)]a_{\overline{20}|j}],=400a_{\overline{{{20}}}|j} \\
a_{\overline{{{20}}}|j} = 5,341.12 / 400 =13.3528
\end{align*}
[[/math]]
Using the financial calculator, [math]j = 0.042[/math] and [math]i=2(0.042)=0.084.[/math]
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