document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170255>Question 1170255</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Nicole will be starting university next fall, she wishes to invest $7000.0 saved from her summer<BR>\n" );
document.write( "job. Her bank offers 2.75% for a one-year term or 2.6% for 6 months and 2.9% for the second six<BR>\n" );
document.write( "months. Which is the better method of investment, 1 year or 2 six month investments? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #795122 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=795122\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if she invests 7000 on a year term, she will have .....\r<BR>\n" );
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document.write( "7000 * 1.0275 ^ 1 = 7192.5 at the end of the 12 month investment.\r<BR>\n" );
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document.write( "if she invests 7000 on two half year terms, she will have.....\r<BR>\n" );
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document.write( "7000 * 1.026 ^ (1/2) = 7090.416067 at the end of the first 6 month investment.\r<BR>\n" );
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document.write( "she will then turn around and invest that amount for the second 6 months to get <BR>\n" );
document.write( "7090.416067 * 1.029 ^ (1/2) = 7192.492336 at the end of the second 6 month investment.\r<BR>\n" );
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document.write( "7192.5 versus 7192.492336 favors the 12 year term investment.<BR>\n" );
document.write( "the difference is very small though.<BR>\n" );
document.write( "7192.5 minus 7192.492336 = .007664.<BR>\n" );
document.write( "that's less than a penny difference.\r<BR>\n" );
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document.write( "the above does not assume monthly compounding of interest.\r<BR>\n" );
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document.write( "if you assume monthly compounding of interest, then:\r<BR>\n" );
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document.write( "if she invests 7000 on a one year term, she will have ....\r<BR>\n" );
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document.write( "7000 * (1 + .0275/12)^12 = 7194.944923 at the end of the 12 month term investment.\r<BR>\n" );
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document.write( "if she invests 7000 on two half year terms, she will have .....\r<BR>\n" );
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document.write( "7000 * (1 + .026/12) ^ 6 = 7091.494343 at the end of the first 6 month investment.\r<BR>\n" );
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document.write( "she will then turn around and invest that amount for the second 6 months to get <BR>\n" );
document.write( "7091.494343 * (1 + .029/12) ^ 6  = 7194.944261 at the end of the second 6 month investment.\r<BR>\n" );
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document.write( "the difference is now 7194.944923 minus 7194.944261 = .006714..\r<BR>\n" );
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document.write( "that's still less than a penny, but the difference is smaller than without monthly compounding.\r<BR>\n" );
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document.write( "the difference is .007664 without monthly compounding and .006714 with monthly compounding.\r<BR>\n" );
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document.write( "in either case, the difference is still less than a penny.\r<BR>\n" );
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document.write( "she could do it either way and be fine with either of them, however, it's simpler to just go with the 12 month investment.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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