document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085860>Question 1085860</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An investment earns 2.25% per annum, compounded daily. The number of years required for the investment to triple in value is... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #699981 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=699981\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\">Use this compound interest formula<BR>\n" );
document.write( "FV = PV*(1+r/n)^(n*t)<BR>\n" );
document.write( "where,<BR>\n" );
document.write( "FV = future value<BR>\n" );
document.write( "PV = present value<BR>\n" );
document.write( "r = interest rate in decimal form<BR>\n" );
document.write( "n = number of times money is compounded per year<BR>\n" );
document.write( "t = time in years\r<BR>\n" );
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document.write( "If we assume that $100 is invested, then we want to know the time t when the future value is $300. So PV = 100 and FV = 300 for some time t. The initial amount invested really doesn't matter because it will cancel out. \r<BR>\n" );
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document.write( "So we have<BR>\n" );
document.write( "FV = 300<BR>\n" );
document.write( "PV = 100<BR>\n" );
document.write( "r = 0.025 (2.25% in decimal form)<BR>\n" );
document.write( "n = 365 (assuming 365 days in a year)<BR>\n" );
document.write( "t = unknown (we're solving for this)\r<BR>\n" );
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document.write( "Plug those values into the formula and solve for t\r<BR>\n" );
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document.write( "FV = PV*(1+r/n)^(n*t)<BR>\n" );
document.write( "300 = 100*(1+0.0225/365)^(365*t)<BR>\n" );
document.write( "300 = 100*(1+0.00006164383562)^(365*t)<BR>\n" );
document.write( "300 = 100*(1.00006164383562)^(365*t)<BR>\n" );
document.write( "300/100 = (1.00006164383562)^(365*t)<BR>\n" );
document.write( "3 = (1.00006164383562)^(365*t)<BR>\n" );
document.write( "Log[3] = Log[(1.00006164383562)^(365*t)]<BR>\n" );
document.write( "Log[3] = (365*t)*Log[1.00006164383562]<BR>\n" );
document.write( "Log[3]/Log[1.00006164383562] = 365*t<BR>\n" );
document.write( "365*t = Log[3]/Log[1.00006164383562]<BR>\n" );
document.write( "365*t = 17822.4819833315<BR>\n" );
document.write( "365*t/365 = 17822.4819833315/365<BR>\n" );
document.write( "t = 48.828717762552\r<BR>\n" );
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document.write( "So it will take <font color=red>roughly 48.828717762552 years</font> for the investment to triple.</font> </SPAN>\n" );
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