document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1023549>Question 1023549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What interest rate is needed in order to double an initial investment of $2000 for two years?<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 #639075 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=639075\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the general equation 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( "in this problem, the time period is years.\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "f = 2 * p = 4000.<BR>\n" );
document.write( "p = 2000<BR>\n" );
document.write( "n = 2<BR>\n" );
document.write( "r = what you want to find.\r<BR>\n" );
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document.write( "the formula becomes 4000 = 2000 * (1 + r) ^ 2\r<BR>\n" );
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document.write( "divide both sides of the equation by 2000 and you get 2 = (1 + r) ^ 2\r<BR>\n" );
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document.write( "take the square root of both sides of the eqution to get sqrt(2) = 1 + r\r<BR>\n" );
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document.write( "subtract 1 from both sides of the equation to get sqrt(2) - 1 = r\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "the decimal equivalent rounded to 5 decimal places is .41421 = r.\r<BR>\n" );
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document.write( "that's pretty close, but won't be right on because sqrt(2) is not a rational number.\r<BR>\n" );
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document.write( "to test it out, you would replace r and evaluate the original formula.\r<BR>\n" );
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document.write( "you would get 4000 = 2000 * (1.141421) ^ 2.\r<BR>\n" );
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document.write( "after evaluation, you would have 4000 = 3999.97984...\r<BR>\n" );
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document.write( "it's close, but no cigar because of the rounding involved.\r<BR>\n" );
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document.write( "if you used 4000 = 2000 * (1 + sqrt(2) - 1) ^ 2, then you would be right on.\r<BR>\n" );
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