document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044475>Question 1044475</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The simple interest on a sum of money in one year is N$50 and compound interest in two years is N$102. Find the sum of money and the rate of interest. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #660114 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=660114\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p = principal<BR>\n" );
document.write( "r = interest rate\r<BR>\n" );
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document.write( "simple interest for 1 year equation is pr = 50\r<BR>\n" );
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document.write( "compound interest equation for 2 years is p * (1+r)^2 - p = 102\r<BR>\n" );
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document.write( "simplify p * (1+r)^2 - p = 102 to get:\r<BR>\n" );
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document.write( "p + 2pr + pr^2 - p = 102\r<BR>\n" );
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document.write( "since plus p and minus p cancel out, you are left with:\r<BR>\n" );
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document.write( "2pr + pr^2 = 102\r<BR>\n" );
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document.write( "solve for p in pr = 50 to get p = 50/r\r<BR>\n" );
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document.write( "replace p with 50/r in 2pr + pr^2 = 102 to get:\r<BR>\n" );
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document.write( "2*50/r*r + 50/r*r^2 = 102\r<BR>\n" );
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document.write( "simplify to get 100 + 50r = 102\r<BR>\n" );
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document.write( "subtract 100 from both sides of the equation to get 50r = 2\r<BR>\n" );
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document.write( "divide both sides of the equation by 50 to get r = 2/50\r<BR>\n" );
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document.write( "r = 2/50 is the same as r = .04\r<BR>\n" );
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document.write( "now that you know r, you can solve for p.\r<BR>\n" );
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document.write( "pr = 50 becomes p * .04 = 50 \r<BR>\n" );
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document.write( "solve for p to get p = 50/.04 = 1250\r<BR>\n" );
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document.write( "p * (1+r)^2 - p = 102 becomes 1250 * (1.04)^2 - 1250 = 102 which becomes 102 = 102\r<BR>\n" );
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document.write( "solution is good.\r<BR>\n" );
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document.write( "p = 1250<BR>\n" );
document.write( "r = .04\r<BR>\n" );
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document.write( " </SPAN>\n" );
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