document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=278791>Question 278791</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a 2000 dollar investment grows to 5000 dollars in 14 years, with interest compounded annually, what is the intrest rate?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #202788 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=202788\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> formula is:\r<BR>\n" );
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document.write( "f = p * (1+i)^n\r<BR>\n" );
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document.write( "f = future value<BR>\n" );
document.write( "p = present amount<BR>\n" );
document.write( "i = annual interest rate compounded annually<BR>\n" );
document.write( "n = number of time periods in years\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "f = 5000<BR>\n" );
document.write( "p = 2000<BR>\n" );
document.write( "i = i<BR>\n" );
document.write( "n = 14\r<BR>\n" );
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document.write( "your formula becomes:\r<BR>\n" );
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document.write( "5000 = 2000 * (1+i)^14\r<BR>\n" );
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document.write( "divide both sides of this formula by 2000 to get:\r<BR>\n" );
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document.write( "5000/2000 = (1+i)^14\r<BR>\n" );
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document.write( "Take the log of both sides of this equation to get:\r<BR>\n" );
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document.write( "log(5000/2000) = log(1+i)^14)\r<BR>\n" );
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document.write( "since log (x^a) = a*log(x), your formula becomes:\r<BR>\n" );
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document.write( "log(5000/2000) = 14 * log(1+i)\r<BR>\n" );
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document.write( "divide both sides of this equation by 14 to get:\r<BR>\n" );
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document.write( "log(1+i) = log(5000/2000)/14\r<BR>\n" );
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document.write( "Use your calculator to find tghe log of (5000/2000) and you get:\r<BR>\n" );
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document.write( "log(1+i) = .397940009/14\r<BR>\n" );
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document.write( "Simplify to get:\r<BR>\n" );
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document.write( "log(1+i) = .028424286\r<BR>\n" );
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document.write( "Use your calculator to find the number whose log is .028424286 and you get:\r<BR>\n" );
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document.write( "1+i = 1.067638647\r<BR>\n" );
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document.write( "Subtract 1 from both sides of this equation to get:\r<BR>\n" );
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document.write( "i = .067638647 which is equivalent to 6.7638647%\r<BR>\n" );
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document.write( "Your annual interest rate is .067638647 which is equivalent to 6.7638647% per year when expressed as a percent.\r<BR>\n" );
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document.write( "Plug this rate (not the percent) back into your original equation, which is:\r<BR>\n" );
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document.write( "5000 = 2000 * (1+i)^14\r<BR>\n" );
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document.write( "replace i with .067638647 to get:\r<BR>\n" );
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document.write( "5000 = 2000 * (1.067638647)^14\r<BR>\n" );
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document.write( "Simplify to get:\r<BR>\n" );
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document.write( "5000 = 2000 * 2.5 = 5000 confirming that the interest rate of .067638647 is good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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