document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173161>Question 1173161</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A 1000$, 4.5% bond with semi annual coupons will be redeemed at the end of 15 years. Find the price to yield (a) 3% </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850752 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=850752\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's calculate the price of the bond step-by-step:\r<BR>\n" );
document.write( "\n" );
document.write( "**Understanding the Bond**\r<BR>\n" );
document.write( "\n" );
document.write( "* **Face Value:** $1,000<BR>\n" );
document.write( "* **Coupon Rate:** 4.5% per year (paid semi-annually)<BR>\n" );
document.write( "* **Yield to Maturity (YTM):** 3% per year (semi-annual yield)<BR>\n" );
document.write( "* **Redemption at Par:** The bond will be redeemed for its face value ($1,000) at maturity.<BR>\n" );
document.write( "* **Time to Maturity:** 15 years\r<BR>\n" );
document.write( "\n" );
document.write( "**Calculations**\r<BR>\n" );
document.write( "\n" );
document.write( "1.  **Semi-annual Coupon Payment:**<BR>\n" );
document.write( "    * Annual coupon payment: $1,000 \* 0.045 = $45<BR>\n" );
document.write( "    * Semi-annual coupon payment: $45 / 2 = $22.50\r<BR>\n" );
document.write( "\n" );
document.write( "2.  **Semi-annual Yield Rate:**<BR>\n" );
document.write( "    * Annual yield rate: 3% or 0.03<BR>\n" );
document.write( "    * Semi-annual yield rate: 0.03 / 2 = 0.015\r<BR>\n" );
document.write( "\n" );
document.write( "3.  **Number of Periods:**<BR>\n" );
document.write( "    * 15 years \* 2 periods/year = 30 periods\r<BR>\n" );
document.write( "\n" );
document.write( "4.  **Bond Pricing Formula:**\r<BR>\n" );
document.write( "\n" );
document.write( "    * Bond Price = (Coupon Payment \* [1 - (1 + Yield Rate)^-Periods]) / Yield Rate + (Face Value / (1 + Yield Rate)^Periods)\r<BR>\n" );
document.write( "\n" );
document.write( "**Applying the Formula**\r<BR>\n" );
document.write( "\n" );
document.write( "**(a) Yield to Maturity of 3%**\r<BR>\n" );
document.write( "\n" );
document.write( "* Bond Price = ($22.50 \* [1 - (1 + 0.015)^-30] / 0.015) + ($1,000 / (1 + 0.015)^30)<BR>\n" );
document.write( "* Bond Price = ($22.50 \* [1 - (1.015)^-30] / 0.015) + ($1,000 / (1.015)^30)<BR>\n" );
document.write( "* Bond Price = ($22.50 \* [1 - 0.638659] / 0.015) + ($1,000 / 1.55816)<BR>\n" );
document.write( "* Bond Price = ($22.50 \* [0.361341] / 0.015) + (641.78)<BR>\n" );
document.write( "* Bond Price = ($22.50 \* 24.0894) + 641.78<BR>\n" );
document.write( "* Bond Price = 542.0115 + 641.78<BR>\n" );
document.write( "* Bond Price = $1183.79 (approximately)\r<BR>\n" );
document.write( "\n" );
document.write( "**Result**\r<BR>\n" );
document.write( "\n" );
document.write( "* (a) The price of the bond to yield 3% is approximately $1,183.79.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );