document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=248918>Question 248918</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How long would it take for an amount of money invested at an annual rate of 6% compounded semiannually, to triple? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #181371 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=181371\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> future value is 3<BR>\n" );
document.write( "present amount is 1<BR>\n" );
document.write( "annual interest rate is 6%\r<BR>\n" );
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document.write( "6% / 2 = 3% every half a year.\r<BR>\n" );
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document.write( "interest rate equals interest rate percent divided by 100% = .03 every half a year.\r<BR>\n" );
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document.write( "the formula you need is:\r<BR>\n" );
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document.write( "3 = 1 * (1.03)^x\r<BR>\n" );
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document.write( "you need to solve for x.\r<BR>\n" );
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document.write( "formula becomes:\r<BR>\n" );
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document.write( "3 = (1.03)^x\r<BR>\n" );
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document.write( "take the log of both sides of the equation to get:\r<BR>\n" );
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document.write( "log(3) = log((1.03)^2)\r<BR>\n" );
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document.write( "by the rules of logarithms, this equation becomes:\r<BR>\n" );
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document.write( "log(3) = x*log(1.03)\r<BR>\n" );
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document.write( "divide both sides of this equation by log(1.03) to get:\r<BR>\n" );
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document.write( "x = log(3)/log(1.03)\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = 37.16700967\r<BR>\n" );
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document.write( "this means that it would take 37.16700967 half years to triple your money.\r<BR>\n" );
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document.write( "divide this by 2 to get:\r<BR>\n" );
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document.write( "18.58350483 years.\r<BR>\n" );
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document.write( "We required half years because our interest rate was every half a year (semi-annually).\r<BR>\n" );
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document.write( "these would be called semi-annual time periods.\r<BR>\n" );
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document.write( "there are 37.16700967 semi-annual time periods which equate to 18.58350483 years.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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