document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197302>Question 1197302</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, please help me solve this problem\r<BR>\n" );
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document.write( "1.If the coupon rate of USD 1000 is 6%, the coupon rate is semiannual, the yield is 5%, and the maturity is 9 years, what is the price?\r<BR>\n" );
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document.write( "2.If the yield rises to 7%, what will the bond price be?\r<BR>\n" );
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document.write( "3.If the yield to maturity is 7%, what is the current bond yield? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848398 by </B><A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><B>ElectricPavlov(122)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><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=848398\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Calculate Bond Price with 5% Yield**\r<BR>\n" );
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document.write( "* **Calculate Semiannual Coupon Payment:**<BR>\n" );
document.write( "    * Annual Coupon Payment = $1000 * 6% = $60<BR>\n" );
document.write( "    * Semiannual Coupon Payment = $60 / 2 = $30\r<BR>\n" );
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document.write( "* **Determine Number of Periods:**<BR>\n" );
document.write( "    * Number of Periods = 9 years * 2 (semiannual) = 18 periods\r<BR>\n" );
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document.write( "* **Calculate Semiannual Yield:**<BR>\n" );
document.write( "    * Semiannual Yield = 5% / 2 = 2.5%\r<BR>\n" );
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document.write( "* **Use the Bond Pricing Formula:**\r<BR>\n" );
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document.write( "   * Bond Price = <BR>\n" );
document.write( "      * (Coupon Payment * [1 - (1 + Semiannual Yield)^-Number of Periods]) / Semiannual Yield <BR>\n" );
document.write( "      * + <BR>\n" );
document.write( "      * (Face Value / (1 + Semiannual Yield)^Number of Periods)\r<BR>\n" );
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document.write( "   * Bond Price = <BR>\n" );
document.write( "      * ($30 * [1 - (1 + 0.025)^-18]) / 0.025 <BR>\n" );
document.write( "      * + <BR>\n" );
document.write( "      * ($1000 / (1 + 0.025)^18)\r<BR>\n" );
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document.write( "   * Bond Price ≈ $30 * 13.7908 + $1000 * 0.6036 <BR>\n" );
document.write( "   * Bond Price ≈ $393.72 + $603.60 <BR>\n" );
document.write( "   * Bond Price ≈ $997.32\r<BR>\n" );
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document.write( "**2. Calculate Bond Price with 7% Yield**\r<BR>\n" );
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document.write( "* **Calculate Semiannual Yield:**<BR>\n" );
document.write( "    * Semiannual Yield = 7% / 2 = 3.5%\r<BR>\n" );
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document.write( "* **Use the Bond Pricing Formula (with the new yield):**\r<BR>\n" );
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document.write( "   * Bond Price = <BR>\n" );
document.write( "      * ($30 * [1 - (1 + 0.035)^-18]) / 0.035 <BR>\n" );
document.write( "      * + <BR>\n" );
document.write( "      * ($1000 / (1 + 0.035)^18)\r<BR>\n" );
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document.write( "   * Bond Price ≈ $30 * 11.9464 + $1000 * 0.4604 <BR>\n" );
document.write( "   * Bond Price ≈ $358.39 + $460.40 <BR>\n" );
document.write( "   * Bond Price ≈ $818.79\r<BR>\n" );
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document.write( "**3. Calculate Current Bond Yield**\r<BR>\n" );
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document.write( "* **Current Bond Yield = (Annual Coupon Payment / Bond Price) * 100%**\r<BR>\n" );
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document.write( "   * **Using the original bond price (from part 1):**<BR>\n" );
document.write( "      * Current Bond Yield = ($60 / $997.32) * 100% ≈ 6.01%\r<BR>\n" );
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document.write( "   * **Using the bond price with the 7% yield (from part 2):**<BR>\n" );
document.write( "      * Current Bond Yield = ($60 / $818.79) * 100% ≈ 7.32%\r<BR>\n" );
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document.write( "**Key Points:**\r<BR>\n" );
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document.write( "* **Bond Prices and Yields:** Bond prices and yields have an inverse relationship. When yields rise, bond prices fall, and vice versa.<BR>\n" );
document.write( "* **Current Yield:** The current yield only considers the annual coupon payment relative to the current bond price. It doesn't account for the time value of money or the bond's maturity.<BR>\n" );
document.write( "* **Yield to Maturity (YTM):** YTM is the overall return anticipated on a bond if it is held until maturity. It considers all future cash flows (coupon payments and principal repayment) and discounts them back to their present value.\r<BR>\n" );
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document.write( "**Disclaimer:** <BR>\n" );
document.write( "* This is a simplified explanation for illustrative purposes. <BR>\n" );
document.write( "* Bond pricing can be complex and may involve other factors like credit risk, liquidity, and market conditions. <BR>\n" );
document.write( "* It's always recommended to consult with a financial professional for investment advice.<BR>\n" );
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