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the following problem is what I am working on.

Suzan can buy a zero coupon bond that will pay $1000$ at the end of $12$ years and is currently selling for $624.60$. Instead she purchases a $6\%$ bond with coupons payable semi-annually that will pay $1000$ at the end of $10$ years. If she pays $X$ she will earn the same annual effective interest rate as the zero coupon bond. Calculate X.

I understand that the effective interest rate per 1/2 a year is $1.98\%$ from the zero coupon bond, but I am not understanding what the other coupon does.

Is the redemption fee $1000$? Is the Future value of the bond $1000$? Either way I did not get the correct answer which is $1167$.

I appreciate any help.

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  • $\begingroup$ Future value is always par removing extreme default events of a business. $\endgroup$
    – dustin
    Commented Jan 13, 2015 at 19:26
  • $\begingroup$ So, I am thinking that if $X$ is what Suzan is going to pay, then the redemption value is also $X$. But if that is the case then she would receive $1.03X=1000$ which does not make sense. $\endgroup$
    – hyg17
    Commented Jan 13, 2015 at 19:30
  • $\begingroup$ Are you saying that $X=578.34(1-(.03-.0198)a_{\overline{20}_.0198})$ ? $\endgroup$
    – hyg17
    Commented Jan 13, 2015 at 19:35
  • $\begingroup$ I appreciate that. I'm more confused where the 1000 comes into play $\endgroup$
    – hyg17
    Commented Jan 13, 2015 at 19:36

1 Answer 1

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With zero coupon bond, using your calculator, when $n = 24$ (bi-annual payments), $i = {}?$, $PV = 624.6$ and $FV = -1000$, we have that $i = 3.96$ which is the bi-annual interest so the interest would be $I = 3.96(2) = 7.92$.

With the 10 year bound, we have that we receive two coupon payments a year totalling $\$60$ so that is two payments of $\$30$. In your calculator, you would enter: \begin{align} n &= 20\\ i &= 3.96\\ PV &= \\ PMT &= -30\\ FV &= -1000 \end{align} Yields the answer you don't agree with. Note that both PMT and FV must carry the same sign since you receive the FV and the PMTs.

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  • $\begingroup$ This is the part that I don't understand. Why do we know that we receive $30$ in each conversion period? I thought that the coupon we receive depends on how much we pay at firs, so doesn't it have to be $Xr=X(.03)$ ? $\endgroup$
    – hyg17
    Commented Jan 13, 2015 at 19:51
  • $\begingroup$ @hyg17 your problem states that the coupon is $6\%$ and par is taking to $\$1000$ unless specified otherwise. So we know for sure $\$60$ a year is received. With bi-annual, it is $60/2=30$. $\endgroup$
    – dustin
    Commented Jan 13, 2015 at 19:53
  • $\begingroup$ Okay so please let me clarify this. In this problem, the par value $F=1000$, the redemption fee is also $C=1000$. The coupon rate $r=6\%$ and the yield rate is what I calculated. $X$ is just the present value of this bond. Am I right? $\endgroup$
    – hyg17
    Commented Jan 13, 2015 at 20:00
  • $\begingroup$ @hyg17 if that is what you call X, I am used to labeling it as PV. $\endgroup$
    – dustin
    Commented Jan 13, 2015 at 20:02
  • $\begingroup$ Thank you very much. I am studying this alone and I see many different ways to represent present values, sometimes its $X$ some times it's $P$ or $PV$. I was not sure what I was looking for in this problem, so I have used $X$. Anyhow, thank you very much. $\endgroup$
    – hyg17
    Commented Jan 13, 2015 at 20:05

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