document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=239772>Question 239772</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An investment with an interest compounded continuously doubled itself in 12 years. What is the interest rate? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #175875 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=175875\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Formula for continuous compounding is:\r<BR>\n" );
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document.write( "FV = PA * e^(rt)\r<BR>\n" );
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document.write( "FV = future value<BR>\n" );
document.write( "PA = present amount<BR>\n" );
document.write( "e = scientific constant of 2.718281828.....<BR>\n" );
document.write( "r = annual interest rate<BR>\n" );
document.write( "t = time in years\r<BR>\n" );
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document.write( "In your equation,\r<BR>\n" );
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document.write( "FV = 2<BR>\n" );
document.write( "PA = 1<BR>\n" );
document.write( "e = 2.71828182818.....<BR>\n" );
document.write( "r = r<BR>\n" );
document.write( "t = 12\r<BR>\n" );
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document.write( "Equation becomes:\r<BR>\n" );
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document.write( "2 = 1 * e^(12r)\r<BR>\n" );
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document.write( "This becomes:\r<BR>\n" );
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document.write( "2 = e^(12r)\r<BR>\n" );
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document.write( "Take natural log of both sides (natural log is log to the base of e)\r<BR>\n" );
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document.write( "ln(2) = ln(e^(12r)\r<BR>\n" );
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document.write( "By laws of logarithms, this becomes:\r<BR>\n" );
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document.write( "ln(2) = 12r*ln(e)\r<BR>\n" );
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document.write( "ln(e) = 1\r<BR>\n" );
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document.write( "Equation becomes:\r<BR>\n" );
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document.write( "ln(2) = 12r\r<BR>\n" );
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document.write( "Divide both sides by 12 to get:\r<BR>\n" );
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document.write( "ln(2)/12 = r\r<BR>\n" );
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document.write( "Solve for r to get:\r<BR>\n" );
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document.write( "r = .057762265 * 100% = 5.7762265%\r<BR>\n" );
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document.write( "Using continuous compounding, an annual interest rate of 5.7762265% will double your money in 12 years.\r<BR>\n" );
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document.write( "Confirm by plugging into the original equation.\r<BR>\n" );
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document.write( "2 = 1 * e^(.057762265*12)\r<BR>\n" );
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document.write( "Simplify to get:\r<BR>\n" );
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document.write( "2 = 2 confirming the value of r is good.\r<BR>\n" );
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document.write( "You might try some of the <a  rel=nofollow HREF= \"http://www.algebra.com/tutors/all-lessons.mpl\" target = \"_blank\">LESSONS FROM ALGEBRA.COM</a> if you have the time.  There's a few in the financial area that might help you.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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