document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=506930>Question 506930</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How long, to the nearest year, will it take me to become a millionaire if I invest $1000 at 9% interest compounded continuously? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #340279 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=340279\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \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 continuous compounding formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000000=1000%2Ae%5E%280.09%2At%29 ALIGN=MIDDLE  ALT=\"1000000=1000%2Ae%5E%280.09%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=1000000 ALIGN=MIDDLE  ALT=\"A=1000000\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=1000 ALIGN=MIDDLE  ALT=\"P=1000\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=0.09 ALIGN=MIDDLE  ALT=\"r=0.09\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the decimal equivalent of 9%).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000000%2F1000=e%5E%280.09%2At%29 ALIGN=MIDDLE  ALT=\"1000000%2F1000=e%5E%280.09%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000 ALIGN=MIDDLE  ALT=\"1000\"   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=1000=e%5E%280.09%2At%29 ALIGN=MIDDLE  ALT=\"1000=e%5E%280.09%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000000%2F1000 ALIGN=MIDDLE  ALT=\"1000000%2F1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000 ALIGN=MIDDLE  ALT=\"1000\"   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=ln%281000%29=ln%28e%5E%280.09%2At%29%29 ALIGN=MIDDLE  ALT=\"ln%281000%29=ln%28e%5E%280.09%2At%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the natural log of both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281000%29=0.09%2At%2Aln%28e%29 ALIGN=MIDDLE  ALT=\"ln%281000%29=0.09%2At%2Aln%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Pull down the exponent using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%5Ey%29=y%2Aln%28x%29%29 ALIGN=MIDDLE  ALT=\"ln%28x%5Ey%29=y%2Aln%28x%29%29\"   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=ln%281000%29=0.09%2At%2A1 ALIGN=MIDDLE  ALT=\"ln%281000%29=0.09%2At%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate the natural log of 'e' to get 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281000%29=0.09%2At ALIGN=MIDDLE  ALT=\"ln%281000%29=0.09%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply and simplify.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.90775527898214=0.09%2At ALIGN=MIDDLE  ALT=\"6.90775527898214=0.09%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate the natural log of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000 ALIGN=MIDDLE  ALT=\"1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.90775527898214 ALIGN=MIDDLE  ALT=\"6.90775527898214\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this value is approximate).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.90775527898214%2F0.09=t ALIGN=MIDDLE  ALT=\"6.90775527898214%2F0.09=t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.09 ALIGN=MIDDLE  ALT=\"0.09\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate 't'.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=76.7528364331349=t ALIGN=MIDDLE  ALT=\"76.7528364331349=t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.90775527898214%2F0.09 ALIGN=MIDDLE  ALT=\"6.90775527898214%2F0.09\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=76.7528364331349 ALIGN=MIDDLE  ALT=\"76.7528364331349\"   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=t=76.7528364331349 ALIGN=MIDDLE  ALT=\"t=76.7528364331349\"   DISABLED_style= \"max-width:90%; height:auto;\" > Flip the equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=77 ALIGN=MIDDLE  ALT=\"t=77\"   DISABLED_style= \"max-width:90%; height:auto;\" > Round to the nearest whole year.\r<BR>\n" );
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document.write( "So it will take roughly 77 years.\r<BR>\n" );
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document.write( "Let me know if you need more help or if you need me to explain a step in more detail.<BR>\n" );
document.write( "Feel free to email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help\">jim_thompson5910@hotmail.com</a><BR>\n" );
document.write( "or you can visit my website here: <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">http://www.freewebs.com/jimthompson5910/home.html</a>\r<BR>\n" );
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document.write( "Thanks,\r<BR>\n" );
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document.write( "Jim  </SPAN>\n" );
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