document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=885944>Question 885944</A>: <I><SPAN STYLE=\"word-break: break-all;\"> you want to invest 10,000 dollars.  how long will it take to double your investment at an annual interest rate of 10% compounded continuously?(round your answer to the nearest year)<BR>\n" );
document.write( "A=Pe </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #535571 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=535571\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One fast shortcut is the <a  rel=nofollow HREF=\"http://en.wikipedia.org/wiki/Rule_of_72\">rule of 72</a>. Divide 72 by 10 (ignore the percent) to get 72/10 = 7.2\r<BR>\n" );
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document.write( "So it takes roughly 7.2 years\r<BR>\n" );
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document.write( "Let's use the formula to get a more accurate answer:\r<BR>\n" );
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document.write( "A = P*e^(r*t)\r<BR>\n" );
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document.write( "20000 = 10000*e^(0.10*t)\r<BR>\n" );
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document.write( "20000/10000 = e^(0.10*t)\r<BR>\n" );
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document.write( "2 = e^(0.10*t)\r<BR>\n" );
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document.write( "ln(2) = ln(e^(0.10*t))\r<BR>\n" );
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document.write( "ln(2) = 0.10*t*ln(e)\r<BR>\n" );
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document.write( "ln(2) = 0.10*t*1\r<BR>\n" );
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document.write( "ln(2) = 0.10*t\r<BR>\n" );
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document.write( "0.10*t = ln(2) \r<BR>\n" );
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document.write( "t = ln(2)/0.10\r<BR>\n" );
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document.write( "t = 6.93147180559946\r<BR>\n" );
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document.write( "t = 7 ... round to the nearest whole number\r<BR>\n" );
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document.write( "So it takes approximately 7 years (which is reasonably close to 7.2)\r<BR>\n" );
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document.write( "The final answer is 7 since they want you to use the formula and round to the nearest year. However, it's always good to know a fast shortcut such as the <a  rel=nofollow HREF=\"http://en.wikipedia.org/wiki/Rule_of_72\">rule of 72</a>. </SPAN>\n" );
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