document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208648>Question 1208648</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Union Local School District has a bond outstanding with a coupon rate of 3.2 percent paid semiannually and 21 years to maturity. The yield to maturity on this bond is 3.5 percent, and the bond has a par value of $5,000. What is the dollar price of the bond?\r<BR>\n" );
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document.write( "Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849187 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849187\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate the bond price:\r<BR>\n" );
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document.write( "**1. Determine the variables:**\r<BR>\n" );
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document.write( "* **Par Value (FV):** $5,000<BR>\n" );
document.write( "* **Coupon Rate:** 3.2% per year (paid semiannually)<BR>\n" );
document.write( "* **Yield to Maturity (YTM):** 3.5% per year (compounded semiannually)<BR>\n" );
document.write( "* **Time to Maturity:** 21 years\r<BR>\n" );
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document.write( "**2. Calculate the semiannual coupon payment:**\r<BR>\n" );
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document.write( "* Semiannual Coupon Payment = (Coupon Rate / 2) * Par Value<BR>\n" );
document.write( "* Semiannual Coupon Payment = (0.032 / 2) * $5,000<BR>\n" );
document.write( "* Semiannual Coupon Payment = $80\r<BR>\n" );
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document.write( "**3. Calculate the number of periods (n):**\r<BR>\n" );
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document.write( "* n = Time to Maturity (in years) * 2 (semiannual periods)<BR>\n" );
document.write( "* n = 21 * 2<BR>\n" );
document.write( "* n = 42\r<BR>\n" );
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document.write( "**4. Calculate the semiannual yield to maturity (r):**\r<BR>\n" );
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document.write( "* r = YTM / 2<BR>\n" );
document.write( "* r = 0.035 / 2<BR>\n" );
document.write( "* r = 0.0175\r<BR>\n" );
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document.write( "**5. Use the present value formula for a bond:**\r<BR>\n" );
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document.write( "Bond Price = (C * [1 - (1 + r)^-n] / r) + (FV / (1 + r)^n)\r<BR>\n" );
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document.write( "Where:\r<BR>\n" );
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document.write( "* C = Semiannual coupon payment<BR>\n" );
document.write( "* r = Semiannual yield to maturity<BR>\n" );
document.write( "* n = Number of periods<BR>\n" );
document.write( "* FV = Par value\r<BR>\n" );
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document.write( "Bond Price = ($80 * [1 - (1 + 0.0175)^-42] / 0.0175) + ($5,000 / (1 + 0.0175)^42)<BR>\n" );
document.write( "Bond Price = ($80 * [1 - 0.5021] / 0.0175) + ($5,000 / 2.0084)<BR>\n" );
document.write( "Bond Price = ($80 * 0.4979 / 0.0175) + $2489.51<BR>\n" );
document.write( "Bond Price = $2276.23 + $2489.51<BR>\n" );
document.write( "Bond Price = $4765.74\r<BR>\n" );
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document.write( "Therefore, the dollar price of the bond is approximately $4765.74.<BR>\n" );
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