document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=920740>Question 920740</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the doubling time for an investment into an account bearing 8.6% interest, compounded monthly. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #558578 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=558578\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f = p * (1+i)^n\r<BR>\n" );
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document.write( "f is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "i is interest rate per time period<BR>\n" );
document.write( "n is the number of time periods.\r<BR>\n" );
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document.write( "in this problem:\r<BR>\n" );
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document.write( "set f = 2 and p = 1<BR>\n" );
document.write( "this means that the future value will be double the present value.\r<BR>\n" );
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document.write( "set i = 8.6 / 100 / 12 = .086 / 12 = .07166666...\r<BR>\n" );
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document.write( "add 1 to that to get 1.0716666...\r<BR>\n" );
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document.write( "best to store it in your calculator so you can work with the full number stored there until you're done, at which time you can round as required.\r<BR>\n" );
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document.write( "n is what you are trying to solve for.\r<BR>\n" );
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document.write( "your equation becomes:\r<BR>\n" );
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document.write( "2 = 1 * (1.0716666...)^n\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "2 = (1.0716666...)^n\r<BR>\n" );
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document.write( "take the log of both sides of this equation to get:\r<BR>\n" );
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document.write( "log(2) = log((1.0716666...)^n)\r<BR>\n" );
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document.write( "since log((1.0716666...)^n) = n * log(1.0716666...), your equation becomes:\r<BR>\n" );
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document.write( "log(2) = n * log(1.0716666...)\r<BR>\n" );
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document.write( "divide both sides of this equation by log (1.0716666...) to get:\r<BR>\n" );
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document.write( "log(2) / log(1.0716666...) = n\r<BR>\n" );
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document.write( "solve for n to get:\r<BR>\n" );
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document.write( "n = 97.06437234\r<BR>\n" );
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document.write( "your money will double in 97.06437234 months.\r<BR>\n" );
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document.write( "divide that by 12 to make it equivalent to 8.088697695 years\r<BR>\n" );
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document.write( "round as you require.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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