document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=255266>Question 255266</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm stuck on the following problem:\r<BR>\n" );
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document.write( "What annual interest rate compounded annually is required to provide a 21% increase in the initial investment after 2 years.\r<BR>\n" );
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document.write( "I tried to use the formula  S = P(1 + i) to the n power.\r<BR>\n" );
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document.write( "I put 10,000 in for P as the original investment (just made it up), then I put 12,100 as S the total investment showing an increase of 21%. Then I filled in 4 for n because the interest is compounded annually! Then try and solve for i\r<BR>\n" );
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document.write( "Not sure if I'm on the right track!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #187534 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=187534\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> looks like you started off ok.\r<BR>\n" );
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document.write( "your formula is:\r<BR>\n" );
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document.write( "S = P * (1+i)^n\r<BR>\n" );
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document.write( "you used 10,000 for P and 1.21 * 10,000 = 12100 for S.\r<BR>\n" );
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document.write( "that's correct but not necessary because you could just as easily have used 1 for P and 1.21 for S.\r<BR>\n" );
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document.write( "I don't know why you filled in 4 for n.\r<BR>\n" );
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document.write( "if compounding is annually, then n should have been 2 to represent 2 years.\r<BR>\n" );
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document.write( "using your numbers for S and P, your formula should have become:\r<BR>\n" );
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document.write( "12100 = 10000 * (1+x)^2\r<BR>\n" );
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document.write( "x is the annual interest rate.\r<BR>\n" );
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document.write( "divide both sides of this equation by 10000 to get:\r<BR>\n" );
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document.write( "1.21 = (1+x)^2\r<BR>\n" );
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document.write( "take the square root of both sides of this equation to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281.21%29+=+1%2Bx ALIGN=MIDDLE  ALT=\"sqrt%281.21%29+=+1%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "subtract 1 from both sidesof this equation to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281.21%29+-+1+=+x ALIGN=MIDDLE  ALT=\"sqrt%281.21%29+-+1+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = .1\r<BR>\n" );
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document.write( "looks like you are looking for 10% a year growth compounded annually for 2 years.\r<BR>\n" );
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document.write( "to confirm, substitute in your original equation to get:\r<BR>\n" );
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document.write( "12100 = 10000 * (1+x)^2 becomes:\r<BR>\n" );
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document.write( "12100 = 10000 * (1.1)^2 \r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "12100 = 12100 confirming the answer is good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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