document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=47662>Question 47662</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534373526/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Which of the given interest rates and compounding periods would provide the better investment?<BR>\n" );
document.write( "(a) 9 1/4% per year, compounded semiannually<BR>\n" );
document.write( "(b) 9% per year, compounded continously\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #31480 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=31480\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consider the result after one year (t=1)\r<BR>\n" );
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document.write( "(a) 9 1/4% per year, compounded semiannually\r<BR>\n" );
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document.write( "A=P(1+0.0925/(2t)^(2t)<BR>\n" );
document.write( "A=P(1+0.04625)^2<BR>\n" );
document.write( "A=P(1.09463906...\r<BR>\n" );
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document.write( "(b) 9% per year, compounded continously<BR>\n" );
document.write( "A=Pe^(0.09t)<BR>\n" );
document.write( "A=Pe^0.09<BR>\n" );
document.write( "A=P(1.09417428...)\r<BR>\n" );
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document.write( "So,for one year the 9 % compounded continuously is growing faster.\r<BR>\n" );
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document.write( "You would have to look at other values of t (maybe by graphing)<BR>\n" );
document.write( "to see which is better in the long run.  I suspect the <BR>\n" );
document.write( "continuous compounding would be the winner.<BR>\n" );
document.write( "To do this, let P be $1.00 and let t=x.\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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