document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193715>Question 1193715</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Topics In Contemporary Math\r<BR>\n" );
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document.write( "   21: Simple Interest\r<BR>\n" );
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document.write( "4) To fix the damage caused by the Springfield Monorail, the city sold $1,000,000 in 20-year bonds that paid a semi-annual coupon with an annual rate of 6.5%. What is the value of each coupon payment? How much interest is paid in total until the bonds are mature? What is the total cost of fixing the damage?\r<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 #848607 by </B><A HREF=/tutors/aboutme.mpl?userid=proyaop><B>proyaop(69)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=proyaop><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=848607\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ### Given Information:<BR>\n" );
document.write( "- **Principal**: \( \$1,000,000 \)<BR>\n" );
document.write( "- **Annual Coupon Rate**: \( 6.5\% \)<BR>\n" );
document.write( "- **Bond Term**: \( 20 \, \text{years} \)<BR>\n" );
document.write( "- **Coupons**: Paid semi-annually.\r<BR>\n" );
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document.write( "### Step 1: Value of Each Coupon Payment\r<BR>\n" );
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document.write( "The value of each coupon payment is calculated as:\r<BR>\n" );
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document.write( "\text{Coupon Payment} = \text{Principal} \times \frac{\text{Annual Coupon Rate}}{\text{Number of Coupons Per Year}}<BR>\n" );
document.write( "\]\r<BR>\n" );
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document.write( "Substituting the values:\r<BR>\n" );
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document.write( "\text{Coupon Payment} = 1,000,000 \times \frac{6.5}{2} \% = 1,000,000 \times 0.0325 = 32,500<BR>\n" );
document.write( "\]\r<BR>\n" );
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document.write( "The value of each coupon payment is **\$32,500**.\r<BR>\n" );
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document.write( "---\r<BR>\n" );
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document.write( "### Step 2: Total Interest Paid Over 20 Years\r<BR>\n" );
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document.write( "The total number of coupon payments over 20 years is:\r<BR>\n" );
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document.write( "\text{Total Payments} = 20 \, \text{years} \times 2 \, \text{payments/year} = 40 \, \text{payments}.<BR>\n" );
document.write( "\]\r<BR>\n" );
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document.write( "The total interest paid is:\r<BR>\n" );
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document.write( "\[<BR>\n" );
document.write( "\text{Total Interest} = \text{Coupon Payment} \times \text{Total Payments}<BR>\n" );
document.write( "\]\r<BR>\n" );
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document.write( "\text{Total Interest} = 32,500 \times 40 = 1,300,000<BR>\n" );
document.write( "\]\r<BR>\n" );
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document.write( "The total interest paid is **\$1,300,000**.\r<BR>\n" );
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document.write( "---\r<BR>\n" );
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document.write( "### Step 3: Total Cost of Fixing the Damage\r<BR>\n" );
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document.write( "The total cost includes the original principal plus all interest payments:\r<BR>\n" );
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document.write( "\text{Total Cost} = \text{Principal} + \text{Total Interest}<BR>\n" );
document.write( "\]\r<BR>\n" );
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document.write( "\text{Total Cost} = 1,000,000 + 1,300,000 = 2,300,000<BR>\n" );
document.write( "\]\r<BR>\n" );
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document.write( "The total cost of fixing the damage is **\$2,300,000**.\r<BR>\n" );
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document.write( "---\r<BR>\n" );
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document.write( "### Final Answers:<BR>\n" );
document.write( "1. **Value of Each Coupon Payment**: **\$32,500**<BR>\n" );
document.write( "2. **Total Interest Paid**: **\$1,300,000**<BR>\n" );
document.write( "3. **Total Cost of Fixing the Damage**: **\$2,300,000** </SPAN>\n" );
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