document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198521>Question 1198521</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How long will it take for $600 to grow to $26,600 at an interest rate of 6.2% if the interest is<BR>\n" );
document.write( "compounded continuously? Round the number of years to the nearest hundredth. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832132 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832132\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> continuous compounding formula is f = p * e ^ (r * t)<BR>\n" );
document.write( "f is the future value<BR>\n" );
document.write( "\p is the present value<BR>\n" );
document.write( "e is the scientific constant of 2.710281828.....<BR>\n" );
document.write( "r is the interest rate per year.<BR>\n" );
document.write( "t is the number of years.\r<BR>\n" );
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document.write( "in your problem, the formula becomes:<BR>\n" );
document.write( "26000 = 600 * e ^ (.062 * t)<BR>\n" );
document.write( "divide both sides of the equaton by 600 to get:<BR>\n" );
document.write( "26000/600 = e ^ (.062 * t)<BR>\n" );
document.write( "take the natural log of both sides of the equation to get:<BR>\n" );
document.write( "ln(26000/600) = ln(e ^ (.062 * t))<BR>\n" );
document.write( "since ln(e ^ (.062 * t)) is equal to .062 * t ln(e) and .062 * t * ln(e) is equal to .062 * t because ln(e) is equal to 1, you get:<BR>\n" );
document.write( "ln(26000/600) = .062 * t<BR>\n" );
document.write( "solve for t to get:<BR>\n" );
document.write( "t = ln(26000/600) / .062 = 60.78906713.\r<BR>\n" );
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document.write( "confirm by replacing 26000 with f and t with 60.7896713 to get:<BR>\n" );
document.write( "f = 600 * e ^ (.062 * 60.7896713)<BR>\n" );
document.write( "solve for f to get:<BR>\n" );
document.write( "f = 26000.<BR>\n" );
document.write( "this confirms the value of t is correct.\r<BR>\n" );
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document.write( "the natural log properties that allow this solution are:<BR>\n" );
document.write( "ln(e^x) = x * ln(e)<BR>\n" );
document.write( "ln(e) = 1\r<BR>\n" );
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document.write( "your solution is it would take 60.79 years for the value of 600 to grow to 26000  when the interest rate of 6.2% is compounded continuously.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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