document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=612930>Question 612930</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the interest rate needed for $6500 to grow to $10400 in 3 years if interest is continously compounded. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #385800 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=385800\">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=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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10400=6500%2Ae%5E%28r%2A3%29 ALIGN=MIDDLE  ALT=\"10400=6500%2Ae%5E%28r%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=10400 ALIGN=MIDDLE  ALT=\"A=10400\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=6500 ALIGN=MIDDLE  ALT=\"P=6500\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3 ALIGN=MIDDLE  ALT=\"t=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10400%2F6500=e%5E%28r%2A3%29 ALIGN=MIDDLE  ALT=\"10400%2F6500=e%5E%28r%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6500 ALIGN=MIDDLE  ALT=\"6500\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.6=e%5E%28r%2A3%29 ALIGN=MIDDLE  ALT=\"1.6=e%5E%28r%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10400%2F6500 ALIGN=MIDDLE  ALT=\"10400%2F6500\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.6 ALIGN=MIDDLE  ALT=\"1.6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281.6%29=ln%28e%5E%28r%2A3%29%29 ALIGN=MIDDLE  ALT=\"ln%281.6%29=ln%28e%5E%28r%2A3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the natural log of both sides.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281.6%29=r%2A3%2Aln%28e%29 ALIGN=MIDDLE  ALT=\"ln%281.6%29=r%2A3%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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281.6%29=r%2A3%2A1 ALIGN=MIDDLE  ALT=\"ln%281.6%29=r%2A3%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate the natural log of 'e' to get 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281.6%29=r%2A3 ALIGN=MIDDLE  ALT=\"ln%281.6%29=r%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply and simplify.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.470003629245736=r%2A3 ALIGN=MIDDLE  ALT=\"0.470003629245736=r%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate the natural log of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.6 ALIGN=MIDDLE  ALT=\"1.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.470003629245736 ALIGN=MIDDLE  ALT=\"0.470003629245736\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this value is approximate).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.470003629245736%2F3=r ALIGN=MIDDLE  ALT=\"0.470003629245736%2F3=r\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate 'r'.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.156667876415245=r ALIGN=MIDDLE  ALT=\"0.156667876415245=r\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.470003629245736%2F3 ALIGN=MIDDLE  ALT=\"0.470003629245736%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.156667876415245 ALIGN=MIDDLE  ALT=\"0.156667876415245\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=0.156667876415245 ALIGN=MIDDLE  ALT=\"r=0.156667876415245\"   DISABLED_style= \"max-width:90%; height:auto;\" > Flip the equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=0.1567 ALIGN=MIDDLE  ALT=\"r=0.1567\"   DISABLED_style= \"max-width:90%; height:auto;\" > Round to the nearest ten-thousandth.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the interest rate is roughly <font color=\"red\">15.67%</font><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );