document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1088346>Question 1088346</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the compound interest formulas  A=P (1 +  r/n)^nt and A=pe^rt<BR>\n" );
document.write( "Suppose that you have $11,000 to invest. Which investment yields the greater return over 5 years: 5.4% compounded monthly or 5.5% compounded quarterly? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #702609 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=702609\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><BR>\n" );
document.write( "We have two investment plans \r<BR>\n" );
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document.write( "Investment Plan A: The money is compounded monthly with annual interest rate of 5.4%<BR>\n" );
document.write( "Investment Plan B: The money is compounded quarterly with annual interest rate of 5.5%\r<BR>\n" );
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document.write( "For both plans A and B, the same amount of money ($11,000) is deposited for the same time duration (5 years).\r<BR>\n" );
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document.write( "For both plans, we'll use the compound interest formula<BR>\n" );
document.write( "A = P(1+r/n)^(n*t)\r<BR>\n" );
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document.write( "where,<BR>\n" );
document.write( "A = amount in the account after t years<BR>\n" );
document.write( "P = initial amount invested<BR>\n" );
document.write( "r = interest rate (in decimal form)<BR>\n" );
document.write( "n = compounding frequency<BR>\n" );
document.write( "t = number of years\r<BR>\n" );
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document.write( "Investment Plan A:\r<BR>\n" );
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document.write( "We invest $11,000 over 5 years at 5.4% compounded monthly\r<BR>\n" );
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document.write( "So this means,<BR>\n" );
document.write( "P = 11000<BR>\n" );
document.write( "r = 0.054 (since 5.4% = 5.4/100 = 0.054)<BR>\n" );
document.write( "n = 12 (monthly ---> compounding 12 times a year)<BR>\n" );
document.write( "t = 5\r<BR>\n" );
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document.write( "Plug all those values into the formula to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+P%281%2Br%2Fn%29%5E%28n%2At%29 ALIGN=MIDDLE  ALT=\"A+=+P%281%2Br%2Fn%29%5E%28n%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+11000%281%2B0.054%2F12%29%5E%2812%2A5%29 ALIGN=MIDDLE  ALT=\"A+=+11000%281%2B0.054%2F12%29%5E%2812%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+11000%281%2B0.0045%29%5E%2812%2A5%29 ALIGN=MIDDLE  ALT=\"A+=+11000%281%2B0.0045%29%5E%2812%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+11000%281.0045%29%5E%2812%2A5%29 ALIGN=MIDDLE  ALT=\"A+=+11000%281.0045%29%5E%2812%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+11000%281.0045%29%5E%2860%29 ALIGN=MIDDLE  ALT=\"A+=+11000%281.0045%29%5E%2860%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+11000%281.30917126694449%29 ALIGN=MIDDLE  ALT=\"A+=+11000%281.30917126694449%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+14400.8839363894 ALIGN=MIDDLE  ALT=\"A+=+14400.8839363894\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+14400.88 ALIGN=MIDDLE  ALT=\"A+=+14400.88\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore, you'll have $14,400.88 in the account if you go with investment plan A. \r<BR>\n" );
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document.write( "Investment Plan B:\r<BR>\n" );
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document.write( "We invest $11,000 over 5 years at 5.5% compounded quarterly\r<BR>\n" );
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document.write( "The values are,<BR>\n" );
document.write( "P = 11000<BR>\n" );
document.write( "r = 0.055 (since 5.5% = 5.5/100 = 0.055)<BR>\n" );
document.write( "n = 4 (quarterly ---> compounding 4 times a year)<BR>\n" );
document.write( "t = 5\r<BR>\n" );
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document.write( "Plug all those values into the formula to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+P%281%2Br%2Fn%29%5E%28n%2At%29 ALIGN=MIDDLE  ALT=\"A+=+P%281%2Br%2Fn%29%5E%28n%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+11000%281%2B0.055%2F4%29%5E%284%2A5%29 ALIGN=MIDDLE  ALT=\"A+=+11000%281%2B0.055%2F4%29%5E%284%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+11000%281%2B0.01375%29%5E%284%2A5%29 ALIGN=MIDDLE  ALT=\"A+=+11000%281%2B0.01375%29%5E%284%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+11000%281.01375%29%5E%284%2A5%29 ALIGN=MIDDLE  ALT=\"A+=+11000%281.01375%29%5E%284%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+11000%281.01375%29%5E%2820%29 ALIGN=MIDDLE  ALT=\"A+=+11000%281.01375%29%5E%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+11000%281.31406650176068%29 ALIGN=MIDDLE  ALT=\"A+=+11000%281.31406650176068%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+14454.7315193675 ALIGN=MIDDLE  ALT=\"A+=+14454.7315193675\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+14454.73 ALIGN=MIDDLE  ALT=\"A+=+14454.73\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore, you'll have $14,454.73 in the account if you go with investment plan B.\r<BR>\n" );
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document.write( "In summary, you'll have...\r<BR>\n" );
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document.write( "<ul><BR>\n" );
document.write( "<li>$14,400.88 in the account if you go with investment plan A.</li><BR>\n" );
document.write( "<li>$14,454.73 in the account if you go with investment plan B.</li><BR>\n" );
document.write( "</ul>\r<BR>\n" );
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document.write( "We see that investment plan B is the winner with the larger amount of money. \r<BR>\n" );
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document.write( " <BR>\n" );
document.write( "</font> </SPAN>\n" );
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