document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173162>Question 1173162</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A 10,000$, 5% with semi annual coupons is price to yield 7%. Find the price if the bond is redeemable at par at the end of (a) 10years, (b) 15years </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850751 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=850751\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break down how to calculate the price of a bond with semi-annual coupons.\r<BR>\n" );
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document.write( "**Understanding the Bond**\r<BR>\n" );
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document.write( "* **Face Value:** $10,000<BR>\n" );
document.write( "* **Coupon Rate:** 5% per year (paid semi-annually)<BR>\n" );
document.write( "* **Yield to Maturity (YTM):** 7% per year (semi-annual yield)<BR>\n" );
document.write( "* **Redemption at Par:** The bond will be redeemed for its face value ($10,000) at maturity.\r<BR>\n" );
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document.write( "**Calculations**\r<BR>\n" );
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document.write( "1.  **Semi-annual Coupon Payment:**<BR>\n" );
document.write( "    * Annual coupon payment: $10,000 \* 0.05 = $500<BR>\n" );
document.write( "    * Semi-annual coupon payment: $500 / 2 = $250\r<BR>\n" );
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document.write( "2.  **Semi-annual Yield Rate:**<BR>\n" );
document.write( "    * Annual yield rate: 7% or 0.07<BR>\n" );
document.write( "    * Semi-annual yield rate: 0.07 / 2 = 0.035\r<BR>\n" );
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document.write( "3.  **Number of Periods:**<BR>\n" );
document.write( "    * (a) 10 years: 10 years \* 2 periods/year = 20 periods<BR>\n" );
document.write( "    * (b) 15 years: 15 years * 2 periods/year = 30 periods\r<BR>\n" );
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document.write( "4.  **Bond Pricing Formula:**\r<BR>\n" );
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document.write( "    * Bond Price = (Coupon Payment \* [1 - (1 + Yield Rate)^-Periods]) / Yield Rate + (Face Value / (1 + Yield Rate)^Periods)\r<BR>\n" );
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document.write( "**Applying the Formula**\r<BR>\n" );
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document.write( "**(a) 10 Years (20 Periods)**\r<BR>\n" );
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document.write( "* Bond Price = ($250 \* [1 - (1 + 0.035)^-20] / 0.035) + ($10,000 / (1 + 0.035)^20)<BR>\n" );
document.write( "* Bond Price = ($250 \* [1 - 0.5025656] / 0.035) + ($10,000 / 1.98978886)<BR>\n" );
document.write( "* Bond Price = ($250 \* 14.212411) + (5025.656)<BR>\n" );
document.write( "* Bond Price = $3553.10275 + $5025.656<BR>\n" );
document.write( "* Bond Price = $8578.76 (approximately)\r<BR>\n" );
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document.write( "**(b) 15 Years (30 Periods)**\r<BR>\n" );
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document.write( "* Bond Price = ($250 \* [1 - (1 + 0.035)^-30] / 0.035) + ($10,000 / (1 + 0.035)^30)<BR>\n" );
document.write( "* Bond Price = ($250 \* [1 - 0.356276] / 0.035) + ($10,000 / 2.80678)<BR>\n" );
document.write( "* Bond Price = ($250 \* 18.392114) + (3562.76)<BR>\n" );
document.write( "* Bond Price = 4598.0285 + 3562.76<BR>\n" );
document.write( "* Bond Price = $8160.79 (approximately)\r<BR>\n" );
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document.write( "**Results**\r<BR>\n" );
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document.write( "* (a) The price of the bond with 10 years to maturity is approximately $8,578.76.<BR>\n" );
document.write( "* (b) The price of the bond with 15 years to maturity is approximately $8,160.79.<BR>\n" );
document.write( " </SPAN>\n" );
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