document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=541357>Question 541357</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What interest rate would be needed to double an investment in 9 years using continuous compounding?<BR>\n" );
document.write( "I tried using the equation A=Principal*e^(rate*time)but am not getting anywhere with it. I would extremely appreciate it if you would include the formula used along with the answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #354183 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=354183\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=Principal%2Ae%5E%28rate%2Atime%29 ALIGN=MIDDLE  ALT=\"A=Principal%2Ae%5E%28rate%2Atime%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Take natural logarithms on both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28A%29=ln%28Principal%29%2Brate%2Atime ALIGN=MIDDLE  ALT=\"ln%28A%29=ln%28Principal%29%2Brate%2Atime\"   DISABLED_style= \"max-width:90%; height:auto;\" > subtract from both sides <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28Principal%29 ALIGN=MIDDLE  ALT=\"ln%28Principal%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28A%29-ln%28Principal%29=rate%2Atime ALIGN=MIDDLE  ALT=\"ln%28A%29-ln%28Principal%29=rate%2Atime\"   DISABLED_style= \"max-width:90%; height:auto;\" > use properties of natural logaritms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28A%2FPrincipal%29=rate%2Atime ALIGN=MIDDLE  ALT=\"ln%28A%2FPrincipal%29=rate%2Atime\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we how we can substitute that doubled the investment bit.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%282%29=rate%2A9 ALIGN=MIDDLE  ALT=\"ln%282%29=rate%2A9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Your calculator or spreadsheet software can calculate <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;\" ><BR>\n" );
document.write( "I calculated <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=rate=ln%282%29%2F9=+0.077016 ALIGN=MIDDLE  ALT=\"rate=ln%282%29%2F9=+0.077016\"   DISABLED_style= \"max-width:90%; height:auto;\" >, meaning annual rate=7.7016%<BR>\n" );
document.write( "Rounding  to 7.7% (or to 7.70%) you end up a few cents short at 9 years, but maybe it's close enough. </SPAN>\n" );
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