document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1147218>Question 1147218</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the amount of money that will be accumulated in an account that pays compound​ interest, given the initial principal of ​$27,800 invested at 2.97​% annual interest for 9 years compounded<BR>\n" );
document.write( "​(a) daily ​(n=365); <BR>\n" );
document.write( "​(b) continuously. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #768543 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=768543\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> discrete compounding formula is f = p * (1 + 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( "continuous compounding formula is f = p * e ^ (r * t)<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( "using the discrete compounding formula, your problem becomes:\r<BR>\n" );
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document.write( "f = 27500 * (1 + .0297/365) ^ (9 * 365) = 35,926.49804.\r<BR>\n" );
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document.write( "using the continuous compounding formula, your problem becomes;\r<BR>\n" );
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document.write( "f = 27500 * e ^ (.0297 * 9) = 35,926.88872.\r<BR>\n" );
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document.write( "we could also have done:\r<BR>\n" );
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document.write( "f = 27500 * e ^ (.0297/365 * 9 * 365) = 35,926.88872.\r<BR>\n" );
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document.write( "since the compounding is continuous, it doesn't matter what time periods we use as long as we're consistant, i.e. r = annual interest rate / number of compounding periods per year paired with n = number of years * number of compounding periods per year.\r<BR>\n" );
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document.write( "also note that daily compounding gets pretty close to continuous compounding.<BR>\n" );
document.write( "the more compounding periods per year you get, the closer you get to continuous compounding results.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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