document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1103250>Question 1103250</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Would you have an investment that pays 5% interest compounded semi –annually or the others investment that pays 5% compounded monthly? Explain your answer. (6m) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #717950 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=717950\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5% interest per year compounding monthly give you more future value than 5% compounding semi-annually.\r<BR>\n" );
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document.write( "the reason has to do with the way that the formula for compound interest works.\r<BR>\n" );
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document.write( "the formula for compound interest is f = p * (1 + r/c) ^ (n*c)\r<BR>\n" );
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document.write( "f is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "r is the annual interest rate<BR>\n" );
document.write( "n is the number of years.<BR>\n" );
document.write( "c is the number of compounding periods per year.\r<BR>\n" );
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document.write( "if you invest 1000 for 20 years at 5% per year compounded semi-annually, the formula becomes:\r<BR>\n" );
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document.write( "f = 1000 * (1 + .05/2) ^ (20*2).\r<BR>\n" );
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document.write( "solve for f to get f = 2685.06\r<BR>\n" );
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document.write( "if you invest 1000 for 20 years at 5% per year compounded monthly, the formula becomes:\r<BR>\n" );
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document.write( "f = 1000 * (1 + .05/12) ^ (20*12).\r<BR>\n" );
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document.write( "solve for f to get f = 2712.64\r<BR>\n" );
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document.write( "compounding 12 times a year gives you a higher effective interest rate than compounding 2 times per year.\r<BR>\n" );
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document.write( "effective interest rate for compounding 2 times per year is (1 + .05/2) ^ 2 - 1 = .050625 per year.\r<BR>\n" );
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document.write( "effective interest rate for compounding 12 times per year is (1 + .05/12) ^ 12 - 1 = .0511618979 per year.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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