document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175042>Question 1175042</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the effective annual yield for each investment. Then select the better investment.  Assume 360 days in a year.\r<BR>\n" );
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document.write( " 5% compounded​ semiannually; 4.9% compounded daily\r<BR>\n" );
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document.write( "The effective annual yield for a 5% compounded semiannually investment is  %. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #800672 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=800672\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5% per year compounded semi-annually is equal to 5% / 100 = .05 per year divided by 2 compounding periods per year = .025 per semi-annual period.\r<BR>\n" );
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document.write( "add 1 to that to get a growth factor of 1.025 per semi-annual time period.\r<BR>\n" );
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document.write( "raise that to the number of compounding periods per year to get 1.025 ^ 2 = 1.050625 - 1 = .050625 * 100 = an effective rate of 5.0625% per year.\r<BR>\n" );
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document.write( "4.9% compounded daily is equal to 4.9% / 100 = .049 per year divided by 360 compounding periods per year = .0001361111111 per daily time period.\r<BR>\n" );
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document.write( "add 1 to that to get a growth factor of 1.000136111 per daily time period.\r<BR>\n" );
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document.write( "raise that to the number of compounding periods per year to get 1.000136111 ^ 360 = 1.050216849 - 1 = .0502168489 * 100 = an effective rate of 5.021684887% per year.\r<BR>\n" );
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document.write( "5% compounded semi-annually give you an effective rate of 5.0625% per year.<BR>\n" );
document.write( "4.9% compounded daily gives you an effective rate of 5.021684887% per year.\r<BR>\n" );
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document.write( "the 5% compounded semi-annually is a better investment than the 4.9% compounded daily because the effective rate per year is higher.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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