document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1144952>Question 1144952</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If you make an investment of ​$3,000 and the investment earns a continuous annual interest rate of 5.5​%, in how much many years will it be worth ​$6000​?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #766182 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=766182\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> continuous compounding formula ia f = p * e ^ (r * n)<BR>\n" );
document.write( "f is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "r is the interest rate per time period<BR>\n" );
document.write( "n is the number of time periods.\r<BR>\n" );
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document.write( "in your problem:<BR>\n" );
document.write( "f = 6000<BR>\n" );
document.write( "p = 3000<BR>\n" );
document.write( "r = .055 per year<BR>\n" );
document.write( "n = number of years.\r<BR>\n" );
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document.write( "formula becomes:<BR>\n" );
document.write( "6000 = 3000 * e ^ (.055 * n)\r<BR>\n" );
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document.write( "divide both sides of this formula by 3000 to get:<BR>\n" );
document.write( "6000 / 3000 = 2 = e ^ ( .055 * n)<BR>\n" );
document.write( "take the natural log of both sides of this equation to get:<BR>\n" );
document.write( "ln(2) = ln(e ^ (.055 * n))<BR>\n" );
document.write( "since ln(e ^ (.055 * n)) = .055 * n * ln(e), and since ln(e) = 1, your formula becomes:<BR>\n" );
document.write( "ln(2) = .055 * n<BR>\n" );
document.write( "divide both sides of this equation by .055 and solve for n to get:<BR>\n" );
document.write( "n = ln(2) / .055 = 12.602675601.\r<BR>\n" );
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document.write( "confirm by replacing n in the original equation by that to get:<BR>\n" );
document.write( "6000 = 3000 * e ^ (.055 * 12.602675601) to get:<BR>\n" );
document.write( "6000 = 6000<BR>\n" );
document.write( "this confirms the value of n is correct.\r<BR>\n" );
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document.write( "your solution is that 3000 will be worth 6000 in 12.601675602 when the continuous compound interest rate is 5.5% per year.\r<BR>\n" );
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