document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175582>Question 1175582</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A hospital administrator deposits $10,000 into an account that earns 9% annual interest compounded monthly. In approximately how many years will the investment be worth $18,000? Round to the nearest whole number. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #801224 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=801224\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> formula to use 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( "in this problem:\r<BR>\n" );
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document.write( "f = 18,000<BR>\n" );
document.write( "p = 10,000<BR>\n" );
document.write( "r = 9% per year divided by 12 = .75% / 100 = .0075 per month<BR>\n" );
document.write( "the formula requires the rate, not the percent.<BR>\n" );
document.write( "n = what you want to find.\r<BR>\n" );
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document.write( "the formula becomes:\r<BR>\n" );
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document.write( "18,000 = 10,000 * 1.0075 ^ n\r<BR>\n" );
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document.write( "divide both sides of the equation by 10,000 to get:\r<BR>\n" );
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document.write( "1.8 = 1.0075 ^ n\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(1.8) = log(1.0075 ^ n)\r<BR>\n" );
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document.write( "by the law of logs that says log(x^n) = n * log(x), the equation becomes:\r<BR>\n" );
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document.write( "log(1.8) = n * log(1.0075)\r<BR>\n" );
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document.write( "divide both sides of the equation by log(1.0075) to get:\r<BR>\n" );
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document.write( "log(1.8) / log(1.0075) = 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 = 78.66508266 months.\r<BR>\n" );
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document.write( "confirm by replacing n in the original equation and solving for f.\r<BR>\n" );
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document.write( "equation becomes f = 10,000 * 1.0075 ^ 78.66508266 = 18,000.\r<BR>\n" );
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document.write( "this confirms the answer is correct.\r<BR>\n" );
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document.write( "divide the number of months by 12 to get 6.55542355 years.\r<BR>\n" );
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document.write( "round to the nearest whole number to get 7.\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "on a graph, it looks like this.\r<BR>\n" );
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document.write( "the number of years is 6.55.....\r<BR>\n" );
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document.write( "that's after the end of the 6th year which puts the solution in the 7th year.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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