document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=235053>Question 235053</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This problem is stumping me.  I have tried to figure out how they come up with the answer with no luck. Any help is greatly appreciated.\r<BR>\n" );
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document.write( "Find the amount that results from the given investment.\r<BR>\n" );
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document.write( "$10 invested at 10% compounded continously after a period of 2 years.  Round to the nearest cent. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #173249 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=173249\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Continuous Compounding is a special formula.\r<BR>\n" );
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document.write( "The formula can be found <a  rel=nofollow HREF= \"http://cs.selu.edu/~rbyrd/math/continuous/\" target = \"_blank\">here !!!!!</a>\r<BR>\n" );
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document.write( "The formula is FV = PA*e^rt\r<BR>\n" );
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document.write( "e is the scientific constant 2.718281828\r<BR>\n" );
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document.write( "FV is the future value of the Amount.\r<BR>\n" );
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document.write( "PA is the present amount.\r<BR>\n" );
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document.write( "r is the interest rate per year.\r<BR>\n" );
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document.write( "t is the amount of time in years.\r<BR>\n" );
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document.write( "For your problem:\r<BR>\n" );
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document.write( "PA = $10.00<BR>\n" );
document.write( "i = 10% per year.<BR>\n" );
document.write( "t = 2\r<BR>\n" );
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document.write( "Formula give you:\r<BR>\n" );
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document.write( "FV = 10*e^(.1*2) = $12.21402758 which equals $12.21 to the nearest cent.\r<BR>\n" );
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document.write( "The closest you can get to continuous compounding without an excessive amount of effort is daily compounding.\r<BR>\n" );
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document.write( "The normal Future Value formula is:\r<BR>\n" );
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document.write( "FV = PA * (1+i)^n where:\r<BR>\n" );
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document.write( "FV = Future Value<BR>\n" );
document.write( "PA = Present Amount<BR>\n" );
document.write( "i = interest rate per time period<BR>\n" );
document.write( "n = number of time periods.\r<BR>\n" );
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document.write( "For a 2 year loan, daily compounding would be calculated as follows:\r<BR>\n" );
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document.write( "i = 10% per year divided by 365 = .02739726% per day.\r<BR>\n" );
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document.write( "That winds up being a daily interest RATE of .0002739726\r<BR>\n" );
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document.write( "The number of timer periods equas the number of years * 365 = 2 * 365 = 730\r<BR>\n" );
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document.write( "Plug that into the formula and you get:\r<BR>\n" );
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document.write( "FV = 10 * (1.0002739726)^730 = $12.213693 which becomes $12.21 \r<BR>\n" );
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document.write( "Continuous compounding got 12.21402 while daily compounding got 12.21369.   That's a pretty close estimate.\r<BR>\n" );
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document.write( "Hourly would get even closer, but daily was ok for a reasonable estimate.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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