document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198838>Question 1198838</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You are investing money at 10.5 percent annual interest, compounded continuously. It will take you ______ years to double your investment. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832568 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=832568\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> continuous compounding formula is f = p * e ^ (r * t)<BR>\n" );
document.write( "f is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "r is the interest rate per time period<BR>\n" );
document.write( "t is the number of time periods.\r<BR>\n" );
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document.write( "in this problem, the time periods are in years.\r<BR>\n" );
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document.write( "formula becomes 2 = 1 * e ^ (.105 * t)<BR>\n" );
document.write( "simplify to get 2 = e ^ (.105 * t)<BR>\n" );
document.write( "take the natural log of both sides of the equation to get:<BR>\n" );
document.write( "ln(2) = ln(e ^ (.105 * t))<BR>\n" );
document.write( "by log rules, this becomes:<BR>\n" );
document.write( "ln(2) = .105 * t * ln(e)<BR>\n" );
document.write( "since ln(e) = 1, this becomes:<BR>\n" );
document.write( "ln(2) = .105 * t<BR>\n" );
document.write( "divide both sides of the equation by .105 to get:<BR>\n" );
document.write( "ln(2) / .105 = t<BR>\n" );
document.write( "solve for t to get:<BR>\n" );
document.write( "t =  6.60140272.\r<BR>\n" );
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document.write( "confirm by replacing t in the original equation to solve for f, to get:<BR>\n" );
document.write( "f = e ^ (.105 * 6.60140272) = 2.<BR>\n" );
document.write( "this confirms the value of t is correct.\r<BR>\n" );
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document.write( "your solution is that it will take 6.60140272 years for you to double your investment.\r<BR>\n" );
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document.write( "this works for any amount of investment.<BR>\n" );
document.write( "for example, if your investment is 500 dollars, then 500 * e ^ (.105 * 6.60140272) will get you 1000 dollars.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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