document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1144914>Question 1144914</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The doubling time of an investment with continuous compound interest is 12.6 years.  If the investment is worth ​$20,000 ​today, how much will it be worth 5 years from​ now?\r<BR>\n" );
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document.write( "It will be worth ​$_ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #766116 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=766116\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula for continuous compounding is f = p * e ^ (r * n).<BR>\n" );
document.write( "the doubling time is given as 12.6 years.<BR>\n" );
document.write( "formula becomes 2 = 1 * e ^ (r * 12.6)<BR>\n" );
document.write( "simplify to:<BR>\n" );
document.write( "2 = e ^ (r * 12.6)<BR>\n" );
document.write( "take the natural log of both sides of this equation to get:<BR>\n" );
document.write( "ln(2) = ln(e ^ (r * 12.6))<BR>\n" );
document.write( "by logarithmic rules, this becomes:<BR>\n" );
document.write( "ln(2) = r * 12.6 * ln(e) which becomes ln(2) = r * 12.6<BR>\n" );
document.write( "solve for r to get r = ln(2) / 12.6 = .055011681\r<BR>\n" );
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document.write( "confirm by replacing r in the original equaton with that to get:<BR>\n" );
document.write( "2 = e ^ (.055011681 * 12.6)<BR>\n" );
document.write( "e ^ (.055011681 * 12.6) = 2, confirming the continuous compounding interest rate is correct.\r<BR>\n" );
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document.write( "that interest rate remain the same, regardless of the number of years, so.....<BR>\n" );
document.write( "f = 20,000 * e ^ (.055011681 * 5) = 26,332.15138.<BR>\n" );
document.write( "that's your solution.\r<BR>\n" );
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document.write( "graphically, the continuoous compounding equation looks like this.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/091101.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "as you can see from the graph, the doubling time is every 12.6 years.<BR>\n" );
document.write( "it went from 20,000 to 40,000 in 12.6 years and then to 80,000 in another 12.6 years.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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