document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1069786>Question 1069786</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If $9,000 is invested at 6% per year compounded monthly, the future value S at any time t (in months) is given by S = 9,000(1.005)t.The amount after 1 year: $9,555.10<BR>\n" );
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document.write( "(b) How long before the investment doubles? (Round your answer to one decimal place.) <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 #685017 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=685017\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula is f = p * (1 + 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( "t is the number of time periods.\r<BR>\n" );
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document.write( "your annual interest rate is .06<BR>\n" );
document.write( "your monthly interest rate is .06/12 = .005.\r<BR>\n" );
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document.write( "if p is 9000, then the amount after 1 year would be.\r<BR>\n" );
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document.write( "f = 9000 * (1.005)^12 = 9555.100307.\r<BR>\n" );
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document.write( "if you want to figure out how long before the money doubles, then do the following.\r<BR>\n" );
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document.write( "f = 2 * 9000 = 18000.\r<BR>\n" );
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document.write( "your formula becomes 18000 = 9000 * (1.005) ^ t.\r<BR>\n" );
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document.write( "now you want to find t.\r<BR>\n" );
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document.write( "divide both sides of the equation by 9000 and you get:\r<BR>\n" );
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document.write( "2 = 1.005 ^ t\r<BR>\n" );
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document.write( "take the log of both sides of the equation to get:\r<BR>\n" );
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document.write( "log(2) = log(1.005 ^ t)\r<BR>\n" );
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document.write( "this is equivalent to:\r<BR>\n" );
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document.write( "log(2) = t * log(1.005)\r<BR>\n" );
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document.write( "divide both sides of this equation by log(1.005) to get:\r<BR>\n" );
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document.write( "log(2) / log(1.005) = t\r<BR>\n" );
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document.write( "solve for t to get:\r<BR>\n" );
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document.write( "t = 138.9757216 months.\r<BR>\n" );
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document.write( "to confirm, replace t with that to get:\r<BR>\n" );
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document.write( "f = 9000 * 1.005 ^ (138.9757216).\r<BR>\n" );
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document.write( "solve for f to get f = 18000.\r<BR>\n" );
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document.write( "that's approximately equal to 11.58 years.\r<BR>\n" );
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