document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1025819>Question 1025819</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help, I am stucked at this question:\r<BR>\n" );
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document.write( "Find the interest rate needed for an investment of $3,000 to grow to an amount of $4,000 in 3 years  if interest is compounded continuously. Please round the answer to the nearest hundredth of percent.\r<BR>\n" );
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document.write( "I am using the compounded interest formula:<BR>\n" );
document.write( "A = P ( 1+&#12310;r/m)&#12311;^mt<BR>\n" );
document.write( "where A = $4000 and P = $3000 and t = 3 (years) and m = 1 (annually) and r = interest (percentage)<BR>\n" );
document.write( "I am stuck at this step: $4000 = $3000 &#12310;(1+r)&#12311;^3<BR>\n" );
document.write( "Suppose if this is correct up to this point, can anyone be kind enough to show me the workings in solving this? Much thanks.<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 #641124 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=641124\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am stuck at this step: $4000 = $3000 * (1+r)^3.\r<BR>\n" );
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document.write( "divide both sides of this equation by 3000 to get:\r<BR>\n" );
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document.write( "4000/3000 = (1+r)^3\r<BR>\n" );
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document.write( "take the third root of both sides of this equation to get:\r<BR>\n" );
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document.write( "(4/3)^(1/3) = 1+r\r<BR>\n" );
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document.write( "subtract 1 from both sides of this equation to get:\r<BR>\n" );
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document.write( "(4/3)^(1/3) - 1 = r\r<BR>\n" );
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document.write( "solve for r to get:\r<BR>\n" );
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document.write( "r = .1006424163.\r<BR>\n" );
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document.write( "multiply by 100 to get r = 10.06424163%.\r<BR>\n" );
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document.write( "round to the nearest tenth to get r = 10.1%\r<BR>\n" );
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document.write( "HOWEVER, .....\r<BR>\n" );
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document.write( "this would not be correct.\r<BR>\n" );
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document.write( "you needed to use the continuous compounding formula.\r<BR>\n" );
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document.write( "that formula is f = p * e^(nr)\r<BR>\n" );
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document.write( "f = future value<BR>\n" );
document.write( "p = present value<BR>\n" );
document.write( "e = scientific constant of 2.71828...<BR>\n" );
document.write( "n = number of time periods.<BR>\n" );
document.write( "r = interest rate per time period.\r<BR>\n" );
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document.write( "that formula would get you:\r<BR>\n" );
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document.write( "4000 = 3000 * e^(3r)\r<BR>\n" );
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document.write( "divide both sides of this equation by 3000 to get:\r<BR>\n" );
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document.write( "4000/3000 = e^(3r)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "4/3 = e^(3r)\r<BR>\n" );
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document.write( "take the natural log of both sides of this equation to get:\r<BR>\n" );
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document.write( "ln(4/3) = ln(e^(3r))\r<BR>\n" );
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document.write( "since ln(e^(3r)) is equal to 3r*ln(e), and since ln(e) = 1, then the equation becomes:\r<BR>\n" );
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document.write( "ln(4/3) = 3r\r<BR>\n" );
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document.write( "divide both sides of the equation by 3 to get:\r<BR>\n" );
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document.write( "ln(4/3)/3 = r\r<BR>\n" );
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document.write( "solve for r to get:\r<BR>\n" );
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document.write( "r = .0958940242\r<BR>\n" );
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document.write( "multiply by 100 to get r = 9.58940242%.\r<BR>\n" );
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document.write( "round to the nearest tenth to get r = 9.6%.\r<BR>\n" );
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document.write( "you needed the continuous compounding formula because the problem stated if interest is compounded continuously.\r<BR>\n" );
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