document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1135947>Question 1135947</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How long does it take an investment of R10 000 to double if it is invested at 8% p.a. compounded annually? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #753662 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=753662\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the investment is doubled, then it will be equal to 20,000.\r<BR>\n" );
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document.write( "formula is 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( "the time periods are in years.\r<BR>\n" );
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document.write( "f = 20,000<BR>\n" );
document.write( "p = 10,000<BR>\n" );
document.write( "r = 8% / 100 = .08\r<BR>\n" );
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document.write( "formula becomes 20,000 = 10,000 * (1 + .08) ^ n\r<BR>\n" );
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document.write( "simplify to get 20,000 = 10,000 * 1.08 ^ n\r<BR>\n" );
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document.write( "divide both sides of this equation by 10,000 to get 20,000 / 10,000 = 1.08 ^ n.\r<BR>\n" );
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document.write( "simplify to get 2 = 1.08 ^ n.\r<BR>\n" );
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document.write( "take the log of both sides of this equation to get log(2) = log(1.08 ^ n)\r<BR>\n" );
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document.write( "since since log(1.08 ^ n) = n * log(1.08), the equation becomes:\r<BR>\n" );
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document.write( "log(2) = n * log(1.08).\r<BR>\n" );
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document.write( "divide both sides of this equation by log(1.08) to get:\r<BR>\n" );
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document.write( "log(2) / log(1.08) = n\r<BR>\n" );
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document.write( "solve for n to get n = 9.006468342\r<BR>\n" );
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document.write( "10,000 * 1.08 ^ 9.006468342 = 20,000, confirming the solution is correct.\r<BR>\n" );
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document.write( "your solution is that the investment will double in 9.006468342 years. </SPAN>\n" );
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