document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=121739>Question 121739</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4)       How long will it take a sum of money to double at 5% per annum compounded continuously?\r<BR>\n" );
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document.write( "a)       5 years\r<BR>\n" );
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document.write( "b)       13.9 years\r<BR>\n" );
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document.write( "c)       16.4 years\r<BR>\n" );
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document.write( "d)       19.1 years\r<BR>\n" );
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document.write( "e)       12.5 years </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89383 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=89383\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Remember the formula for compounding interest continuously is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=Pe%5E%28rt%29 ALIGN=MIDDLE  ALT=\"A=Pe%5E%28rt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where A is the return, P is the principal, r is the interest rate and t is the time\r<BR>\n" );
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document.write( "So if we want to know when our money will double, this means that A will be twice as much as P. In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2P ALIGN=MIDDLE  ALT=\"A=2P\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=Pe%5E%28rt%29 ALIGN=MIDDLE  ALT=\"A=Pe%5E%28rt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2P=Pe%5E%280.05t%29 ALIGN=MIDDLE  ALT=\"2P=Pe%5E%280.05t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2P ALIGN=MIDDLE  ALT=\"A=2P\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=0.05 ALIGN=MIDDLE  ALT=\"r=0.05\"   DISABLED_style= \"max-width:90%; height:auto;\" > note: 5% is the decimal number 0.05\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2P%2FP=e%5E%280.05t%29 ALIGN=MIDDLE  ALT=\"2P%2FP=e%5E%280.05t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by P\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=e%5E%280.05t%29 ALIGN=MIDDLE  ALT=\"2=e%5E%280.05t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%282%29=0.05t ALIGN=MIDDLE  ALT=\"ln%282%29=0.05t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the natural log of both sides. This will eliminate the base \"e\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%282%29%2F0.05=t ALIGN=MIDDLE  ALT=\"ln%282%29%2F0.05=t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 0.05 to isolate t\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.69315%2F0.05=t ALIGN=MIDDLE  ALT=\"0.69315%2F0.05=t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use a calculator to evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%282%29 ALIGN=MIDDLE  ALT=\"ln%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Note: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%282%29=0.69315 ALIGN=MIDDLE  ALT=\"ln%282%29=0.69315\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13.863=t ALIGN=MIDDLE  ALT=\"13.863=t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide \r<BR>\n" );
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document.write( "Now if you round to the nearest hundredth, the answer is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=13.9 ALIGN=MIDDLE  ALT=\"t=13.9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So it will take about 13.9 years to double any given sum of money\r<BR>\n" );
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document.write( "So the answer is B) </SPAN>\n" );
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