document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=350478>Question 350478</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The U.S. Treasury offers to sell you a bond for $613.81 no payments will be made until the bond matures 10 years from now at which time it will be redeemed for $1,000. What interest rate would you earn if you bought this bond at the offer price </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #250563 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=250563\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You pay $613.81 for the bond.<BR>\n" );
document.write( "You get $1,000 back in 10 years.\r<BR>\n" );
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document.write( "With annual compounding, your money has earned 5.001766149% per year.\r<BR>\n" );
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document.write( "The yearly increase in the investment is shown below:\r<BR>\n" );
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document.write( "YEAR	BALANCE\r\n" );
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document.write( "0	$613.81\r\n" );
document.write( "1	$644.51\r\n" );
document.write( "2	$676.75\r\n" );
document.write( "3	$710.60\r\n" );
document.write( "4	$746.14\r\n" );
document.write( "5	$783.46\r\n" );
document.write( "6	$822.65\r\n" );
document.write( "7	$863.79\r\n" );
document.write( "8	$907.00\r\n" );
document.write( "9	$952.36\r\n" );
document.write( "10	$1,000.00\r\n" );
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document.write( "You start off with 613.81.\r<BR>\n" );
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document.write( "You multiply that by 1.05001766149 each year for 10 years and wind up with $1,000 at the end of it.\r<BR>\n" );
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document.write( "The factor 1.05001766149 is derived as follows:\r<BR>\n" );
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document.write( "5.001766149% divided by 100% = .05001766149\r<BR>\n" );
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document.write( "That's the interest rate per year.\r<BR>\n" );
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document.write( "The value of the investment in the next year is equal to the investment in that year + the investment in that year times the interest rate.\r<BR>\n" );
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document.write( "That would be 613.81 + 613.81 * .05001766149\r<BR>\n" );
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document.write( "You take out the common factor in this to get:\r<BR>\n" );
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document.write( "613.81 * (1 + .05001766149) which becomes:\r<BR>\n" );
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document.write( "613.81 * 1.05001766149.\r<BR>\n" );
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document.write( "That's the growth in the first year.\r<BR>\n" );
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document.write( "With compounding, the same formula is applied to the new value in the next year, and the next year, and the next year, up until you reach year 10.\r<BR>\n" );
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document.write( "The money you receive from the bond in 10 years is equivalent to investing the $613.81 in an account that is paying you 5.001766149% per year compounded annually.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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