document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1072014>Question 1072014</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Matt invest $500 into an account with a 7.5% interest rate compounded yearly. How long will it be until the account has a value of $2500? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #687206 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=687206\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f = p * (1+r) ^ n\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( "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( "your time period is years.\r<BR>\n" );
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document.write( "you are given that:\r<BR>\n" );
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document.write( "i = 7.5% per year / 100 = .075 per year.\r<BR>\n" );
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document.write( "p = 500\r<BR>\n" );
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document.write( "f = 2500\r<BR>\n" );
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document.write( "f = p * (1+r) ^ n becomes 2500 = 500 * 1.075 ^ n\r<BR>\n" );
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document.write( "divide both sides of this equation by 500 to get:\r<BR>\n" );
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document.write( "2500 / 500 = 1.075 ^ n\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "5 = 1.075 ^ n\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(5) = log(1.075 ^ n)\r<BR>\n" );
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document.write( "since log(a^b) = b * log(a), your equation becomes:\r<BR>\n" );
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document.write( "log(5) = n * log(1.075)\r<BR>\n" );
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document.write( "divide both sides of this equation by log(1.075) to get:\r<BR>\n" );
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document.write( "log(5) / log(1.075) = n\r<BR>\n" );
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document.write( "solve for n to get:\r<BR>\n" );
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document.write( "n = 22.25419233\r<BR>\n" );
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document.write( "confirm by replacing n in the original equation and evaluating to see that the equation is true.\r<BR>\n" );
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document.write( "2500 = 500 * 1.075 ^ n becomes 2500 = 500 * 1.075 ^ 22.25419233.\r<BR>\n" );
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document.write( "evaluate to get 2500 = 2500.\r<BR>\n" );
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document.write( "this confirms the solution is good.\r<BR>\n" );
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document.write( "the solution is that it will take 22.25419233 year for 500 to become 2500 at an interest rate of 7.5% compounded annually.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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