document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189665>Question 189665</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Compounded semi-annually.  P dollars is invested at annual interest rate r for 1 year.  If the interest is compounded semiannually, then the polynomial P(1 + r/2)^2 represents the value of the investment after 1 year.  Rewrite this expression without parenthesis.  Evaluate the polynomial if P=$200 and r = 10%.\r<BR>\n" );
document.write( "\n" );
document.write( "this is the answer I got<BR>\n" );
document.write( "a.	P + 2²P+ Pr²\r<BR>\n" );
document.write( "\n" );
document.write( "       b.  200(1+ 10/100.2)^2<BR>\n" );
document.write( "             200(1+0.05)^2 = 200 multiply 0.0025  =$50.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142306 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=142306\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%281+%2B+r%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"P%281+%2B+r%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%281%2B2%28r%2F2%29%2Br%5E2%2F4%29 ALIGN=MIDDLE  ALT=\"P%281%2B2%28r%2F2%29%2Br%5E2%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%281%2Br%2Br%5E2%2F4%29 ALIGN=MIDDLE  ALT=\"P%281%2Br%2Br%5E2%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2BPr%2BP%28r%5E2%2F4%29%29 ALIGN=MIDDLE  ALT=\"P%2BPr%2BP%28r%5E2%2F4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28r%5E2%2F4%29%2BPr%2BP ALIGN=MIDDLE  ALT=\"P%28r%5E2%2F4%29%2BPr%2BP\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "There are two ways to do this:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Method #1:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%281+%2B+r%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"P%281+%2B+r%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the original expression\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%281+%2B+0.1%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"200%281+%2B+0.1%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=200 ALIGN=MIDDLE  ALT=\"P=200\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=0.1 ALIGN=MIDDLE  ALT=\"r=0.1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%281+%2B+0.05%29%5E2 ALIGN=MIDDLE  ALT=\"200%281+%2B+0.05%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%281.05%29%5E2 ALIGN=MIDDLE  ALT=\"200%281.05%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%281.1025%29 ALIGN=MIDDLE  ALT=\"200%281.1025%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 1.05 to get 1.1025\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=220.5 ALIGN=MIDDLE  ALT=\"220.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So after a year, we have $220.50 in the account\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Method #2:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28r%5E2%2F4%29%2BPr%2BP ALIGN=MIDDLE  ALT=\"P%28r%5E2%2F4%29%2BPr%2BP\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the expanded polynomial (from part a)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%280.1%5E2%2F4%29%2B200%280.1%29%2B200 ALIGN=MIDDLE  ALT=\"200%280.1%5E2%2F4%29%2B200%280.1%29%2B200\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=200 ALIGN=MIDDLE  ALT=\"P=200\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=0.1 ALIGN=MIDDLE  ALT=\"r=0.1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%280.01%2F4%29%2B200%280.1%29%2B200 ALIGN=MIDDLE  ALT=\"200%280.01%2F4%29%2B200%280.1%29%2B200\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 0.1 to get 0.01\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%280.0025%29%2B200%280.1%29%2B200 ALIGN=MIDDLE  ALT=\"200%280.0025%29%2B200%280.1%29%2B200\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5%2B20%2B200 ALIGN=MIDDLE  ALT=\"0.5%2B20%2B200\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=220.5 ALIGN=MIDDLE  ALT=\"220.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So using either method, we get $220.5<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );