document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140562>Question 1140562</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How long does it take for $1875 to double if it is invested at 10% compounded continuously? Round your answer to two decimal places, if necessary. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #761085 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=761085\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the continuous compounding formula is f = p * e ^ (r * t)\r<BR>\n" );
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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 equal to 2.718281828.....<BR>\n" );
document.write( "r is the interest rate per time period<BR>\n" );
document.write( "t is the number of time periods\r<BR>\n" );
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document.write( "the time period for this problem will be in years.\r<BR>\n" );
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document.write( "in this problem, .....<BR>\n" );
document.write( "future value is double the present value = 3750<BR>\n" );
document.write( "present value is 1875<BR>\n" );
document.write( "interest rate per time period is 10% / 100 = .10<BR>\n" );
document.write( "number of time periods is what you want to find.\r<BR>\n" );
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document.write( "f = p * e ^ (r * t) becomes:\r<BR>\n" );
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document.write( "3750 = 1875 * e ^ (.10 * t)\r<BR>\n" );
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document.write( "divide both sides of this equation by 1875 to get:\r<BR>\n" );
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document.write( "3750/1875 = e ^ (.10 * t)\r<BR>\n" );
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document.write( "simplify and take the natural log of both sides of the equation to get:\r<BR>\n" );
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document.write( "ln(2) = ln(e ^ (.10 * t)\r<BR>\n" );
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document.write( "since ln(e ^ (.10 * t) = .10 * t * ln(e) and since ln(e) = 1, the equation becomes:\r<BR>\n" );
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document.write( "ln(2) = .10 * t \r<BR>\n" );
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document.write( "solve for t to get t = ln(2) / .10 = 6.931471806 years.\r<BR>\n" );
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document.write( "the money will double in 6.931471806 years.\r<BR>\n" );
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document.write( "confirm by replacing t with 6.931471806 in the original equation to get:\r<BR>\n" );
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document.write( "3750 = 1875 * e ^ (.10 * 6.931471806) becomes 3750 = 3750.\r<BR>\n" );
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document.write( "this confirms the solution is correct.\r<BR>\n" );
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document.write( "your solution is it will take 6.93 years for the money to double.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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