document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=935622>Question 935622</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PLEASE HELP ME IF ANY ONE CAN....... AND TELL ME TOO ACTUALLY WHAT ARE THEY ASKING ABOUT  MAY BE I AM NOT GETTING THE QUESTION.....<BR>\n" );
document.write( "THE DIFFERENCE BETWEEN COMPOUND INTEREST AND SIMPLE INTEREST AT THE RATE FOR $5000 FOR 2 YEARS IS $72.FIND THE RATE OF INTEREST p.a.? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #568866 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=568866\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> THE DIFFERENCE BETWEEN COMPOUND INTEREST AND SIMPLE INTEREST AT THE RATE FOR $5000 FOR 2 YEARS IS $72.  FIND THE RATE OF INTEREST p.a.?\r<BR>\n" );
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document.write( "equation for simple interest is i = n * r * p\r<BR>\n" );
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document.write( "equation for compound interest is i = p * (1+ r)^n - p\r<BR>\n" );
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document.write( "you are being told that the difference between them after 2 years is equal to 72.\r<BR>\n" );
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document.write( "replace what you know in both equations.\r<BR>\n" );
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document.write( "i = n * r * p becomes i = 2 * r * 5000\r<BR>\n" );
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document.write( "i = p * (1 + r)^n - p becomes i = 5000 * (1 + r)^2 - 5000\r<BR>\n" );
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document.write( "the difference between them is 72.<BR>\n" );
document.write( "compound interest will be greater than simple interest.<BR>\n" );
document.write( "the equation you now want to solve is:\r<BR>\n" );
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document.write( "5000 * (1 + r)^2 - 5000 - (2 * r * 5000) = 72\r<BR>\n" );
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document.write( "you need to use this equation to solve for r.\r<BR>\n" );
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document.write( "simplify the equation to get:\r<BR>\n" );
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document.write( "5000 * (1 + r)^2 - 5000 - 10000 * r = 72\r<BR>\n" );
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document.write( "since (1 + r)^2 = r^2 + 2r + 1, then your equation becomes:\r<BR>\n" );
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document.write( "5000 * (r^2 + 2r + 1) - 5000 - 10000 * r = 72\r<BR>\n" );
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document.write( "distribute the multiplication to get:\r<BR>\n" );
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document.write( "5000 * r^2 + 10000 * r + 5000 - 5000 - 10000 * r = 72\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "5000 * r^2 = 72\r<BR>\n" );
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document.write( "divide both sides of this equation by 5000 to get:\r<BR>\n" );
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document.write( "r^2 = 72 / 5000\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( "r = plus or minus sqrt(72/5000) = .12\r<BR>\n" );
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document.write( "your interest rate is 12%.\r<BR>\n" );
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document.write( "with simple interest, i = n * r * p becomes i = 2 * .12 * 5000 which becomes i =  1200\r<BR>\n" );
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document.write( "with compound interest, i = p * (1 + r)^n - p becomes i = 5000 * (1.12)^2 - 5000 which becomes i = 6272 - 5000 which becomes i = 1272.\r<BR>\n" );
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document.write( "the difference between them is 1272 - 1200 = 72.\r<BR>\n" );
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document.write( "the solution is that r = .12 and it is confirmed to be good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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