document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083905>Question 1083905</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Union Local School District has a bond outstanding with a coupon rate of 3.7% paid semiannually and 16 years to maturity. The yield to maturity of the bond is 3.9%, and the bond has a par value of $5000. What is the price of the bond?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #698248 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=698248\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"4\"><BR>\n" );
document.write( "Answer: <font color=red>$4,881.80</font><BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "Refer to the PDF at the link below<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://people.ucsc.edu/~lbaum/econ80h/LS-Chap010.pdf\">https://people.ucsc.edu/~lbaum/econ80h/LS-Chap010.pdf</a><BR>\n" );
document.write( "Specifically turn to page 6 for the formula we'll use. <BR>\n" );
document.write( "An example is shown on page 7.\r<BR>\n" );
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document.write( "The formula we're using is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \text{Bond Price} = \frac{C}{\text{YTM}}*\left[1 - \frac{1}{\left(1+\text{YTM}/2\right)^{2*M}}\right] + \frac{FV}{\left(1+\text{YTM}/2\right)^{2*M}}\"><BR>\n" );
document.write( "where<BR>\n" );
document.write( "C = annual coupon payment (in dollars)<BR>\n" );
document.write( "YTM = Yield To Maturity (expressed in decimal form)<BR>\n" );
document.write( "M = Maturity of the bond (in years)<BR>\n" );
document.write( "FV = face value of the bond (aka the par value in dollars)\r<BR>\n" );
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document.write( "In this case,<BR>\n" );
document.write( "C = (coupon rate)*(Par value) = (3.7/100)*5000 = 185 dollars<BR>\n" );
document.write( "YTM = (3.9/100) = 0.039<BR>\n" );
document.write( "M = 16 years<BR>\n" );
document.write( "FV = 5000 dollars\r<BR>\n" );
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document.write( "which are plugged into the formula to get...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \text{Bond Price} = \frac{C}{\text{YTM}}*\left[1 - \frac{1}{\left(1+\text{YTM}/2\right)^{2*M}}\right] + \frac{FV}{\left(1+\text{YTM}/2\right)^{2*M}}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \text{Bond Price} = \frac{185}{\text{0.039}}*\left[1 - \frac{1}{\left(1+\text{0.039}/2\right)^{2*16}}\right] + \frac{5000}{\left(1+\text{0.039}/2\right)^{2*16}}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \text{Bond Price} = 4743.58974358974*\left[1 - \frac{1}{\left(1+0.0195\right)^{32}}\right] + \frac{5000}{\left(1+0.0195\right)^{32}}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \text{Bond Price} = 4743.58974358974*\left[1 - \frac{1}{\left(1.0195\right)^{32}}\right] + \frac{5000}{\left(1.0195\right)^{32}}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \text{Bond Price} = 4743.58974358974*\left[1 - \frac{1}{1.85520268276352}\right] + \frac{5000}{1.85520268276352}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \text{Bond Price} = 4743.58974358974*\left[1-0.539024662529268\right] + 2695.12331264634\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \text{Bond Price} = 4743.58974358974*0.460975337470732 + 2695.12331264634\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \text{Bond Price} = 2186.67788287399 + 2695.12331264634\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \text{Bond Price} = 4881.80119552033\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \text{Bond Price} = 4881.80\">\r<BR>\n" );
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document.write( "So the bond price is roughly <font color=red>$4,881.80</font><BR>\n" );
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