document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187352>Question 1187352</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 11.	Ten years ago the Jamaica Nice Company issued a 30-year bond with a $1,000 par value. to the public. The bonds have a 10.50% annual coupon rate. If investors require a yield to maturity of 9.0% what is the current price of the bonds? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849312 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=849312\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate the current price of the bond:\r<BR>\n" );
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document.write( "**1. Determine the remaining years to maturity:**\r<BR>\n" );
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document.write( "* The bond was issued 10 years ago and had a 30-year maturity.<BR>\n" );
document.write( "* Therefore, there are 20 years remaining until the bond matures.\r<BR>\n" );
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document.write( "**2. Calculate the annual coupon payment:**\r<BR>\n" );
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document.write( "* Coupon rate = 10.50%<BR>\n" );
document.write( "* Par value = $1,000<BR>\n" );
document.write( "* Annual coupon payment = 0.105 * $1,000 = $105\r<BR>\n" );
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document.write( "**3. Use the present value formula for a bond:**\r<BR>\n" );
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document.write( "The current price of the bond is the present value of all future cash flows (coupon payments and par value) discounted at the yield to maturity.\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 = Annual coupon payment ($105)<BR>\n" );
document.write( "* r = Yield to maturity (9.0% or 0.09)<BR>\n" );
document.write( "* n = Number of years to maturity (20)<BR>\n" );
document.write( "* FV = Face value or par value of the bond ($1,000)\r<BR>\n" );
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document.write( "**4. Plug the values into the formula:**\r<BR>\n" );
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document.write( "Bond Price = ($105 * [1 - (1 + 0.09)^-20] / 0.09) + ($1,000 / (1 + 0.09)^20)\r<BR>\n" );
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document.write( "**5. Calculate the present value of the coupon payments:**\r<BR>\n" );
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document.write( "* (1 + 0.09)^-20 ≈ 0.1784<BR>\n" );
document.write( "* 1 - 0.1784 ≈ 0.8216<BR>\n" );
document.write( "* $105 * 0.8216 / 0.09 ≈ $956.11\r<BR>\n" );
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document.write( "**6. Calculate the present value of the par value:**\r<BR>\n" );
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document.write( "* $1,000 / (1 + 0.09)^20 ≈ $178.41\r<BR>\n" );
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document.write( "**7. Add the present values together:**\r<BR>\n" );
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document.write( "Bond Price ≈ $956.11 + $178.41 ≈ $1,134.52\r<BR>\n" );
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document.write( "**Therefore, the current price of the bond is approximately $1,134.52.**<BR>\n" );
document.write( " </SPAN>\n" );
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