document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140029>Question 1140029</A>: <I><SPAN STYLE=\"word-break: break-all;\">  At what rate do you need to invest money into a bank account earning continuously compounded interest if you want to double your money in 62 months? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #760481 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=760481\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> continuous compounding formula is f = p * e ^ (r * t)\r<BR>\n" );
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document.write( "if you want to double your money, then left f = 2 and p = 1.\r<BR>\n" );
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document.write( "formula becomes 2 = 1 * e ^ (r * t)\r<BR>\n" );
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document.write( "this is the same as 2 = e ^ (r * t)\r<BR>\n" );
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document.write( "if you want to do it in 62 months, then the formula becomes 2 = e ^ (r * 62).\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(2) = ln(e ^ (r * 62)\r<BR>\n" );
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document.write( "since ln(e ^ (r * 62) is equal to r * 62 * ln(e) and since ln(e) is equal to 1, your formula becomes:\r<BR>\n" );
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document.write( "ln(2) = r * 62\r<BR>\n" );
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document.write( "divide both sides of this formula by 62 to get:\r<BR>\n" );
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document.write( "ln(2) / 62 = 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 = .0111797932\r<BR>\n" );
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document.write( "replace r in the original equation to get:\r<BR>\n" );
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document.write( "2 = e ^ (.0111797932 * 62)\r<BR>\n" );
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document.write( "this becomes 2 = 2, confirming the solution is correct.\r<BR>\n" );
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document.write( "your interest rate is .0111797932 * 12 = .1341575188 per year.\r<BR>\n" );
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document.write( "that's approximately 13.42% per year.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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