document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1141245>Question 1141245</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 13. An amount of $2000 earns $400 interest in 3 years and 2 months. What is the effective annual rate of interest compounds monthly?<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 #761766 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=761766\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f = p * (1 + r) ^ n<BR>\n" );
document.write( "i = f - p<BR>\n" );
document.write( "f = p * i\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( "i is the interest<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( "f = p + i = 2000 + 400 = 2400<BR>\n" );
document.write( "p = 2000<BR>\n" );
document.write( "n = 3 years * 12 = 36 months + 2 = 38 months\r<BR>\n" );
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document.write( "formula becomes 2400 = 2000 * (1 + r) ^ 38\r<BR>\n" );
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document.write( "divide both sides of the equation by 2000 to get 2400 / 2000 = (1 + r) ^ 38\r<BR>\n" );
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document.write( "take the 38th root of both sides of the equation to get (2400/2000) ^ (1/38) = 1 + r.\r<BR>\n" );
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document.write( "subtract 1 from both sides of the equation to get (2400/2000) ^ (1/38) - 1 = r\r<BR>\n" );
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document.write( "solve for r to get r = .0048094642\r<BR>\n" );
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document.write( "replace r with that in the original equation to confirms that it works.\r<BR>\n" );
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document.write( "original equation becomes 2400 = 2000 * (1 + .0048094642) ^ 38 which becomes 2400 = 2400, confirming the solution is good.\r<BR>\n" );
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document.write( "the nominal annual interest rate is .0048094642 * 12 = .0577135707 * 100 = 5.77135707%.\r<BR>\n" );
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document.write( "the effective annual interest rate is (1 + .0048094642) ^ 12 = 1.059264955 - 1 = .0592649545 * 100 = 5.92649545%.\r<BR>\n" );
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