document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=558613>Question 558613</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am a little confused about this one.  Can someone help me? \r<BR>\n" );
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document.write( "   Investing is an important topic for individuals in all areas. Suppose you wish to invest $10,000 in a money market account that earns 4% interest compounded annually. How much would the investment be worth after 10 years? Show all calculations.<BR>\n" );
document.write( "    Now, suppose that the above investment earns interest compounded quarterly. How much would the same investment be worth after 10 years? Why does the result differ from the previous one?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #363130 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=363130\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> With annual compounding, the $10,000 deposit would earn $400 in interest the first year. (A $100 interest would be earned each quarter, but that extra money would not be accruing extra interest during the first year).<BR>\n" );
document.write( "At the beginning of the second year, the balance would be $10,400, and interest would be calculated based on that new balance for the whole second year.<BR>\n" );
document.write( "For each of the 10 years the balance at the beginning of the year would be multiplied times 1.04 by the end of the year: each $100 would turn into $104.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.04=%28100%2B4%29%2F100 ALIGN=MIDDLE  ALT=\"1.04=%28100%2B4%29%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "After 10 years the balance would be<BR>\n" );
document.write( "$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000%2A1.04%5E10 ALIGN=MIDDLE  ALT=\"10000%2A1.04%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" > = $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14802.44 ALIGN=MIDDLE  ALT=\"14802.44\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If the interest were compounded quarterly, after 3 month, you would have an extra $100, just like before, for a total of $10,100, but interest would start accruing on the whole $10,100 for the second quarter. So, during the second quarter you would get another $100 in interest from the initial $10,000, plus an extra $1 from the interest on the $100 earned on the first quarter. During the third quarter, you would get interest on the whole $10,201. You would get another $100 from the initial $10,000, but you would also earn $2.01 on the $201 interest earned in the previous 2 quarters. Each quarter, it would get better. The balance at the beginning of the quarter would be multiplied by 1.01 at the end of the quarter. At the end of the first year, the balance would be<BR>\n" );
document.write( "$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000%2A1.01%5E4 ALIGN=MIDDLE  ALT=\"10000%2A1.01%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10406.04 ALIGN=MIDDLE  ALT=\"10406.04\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Because of the quarterly compounding, you would be $6.04 ahead after just one year.<BR>\n" );
document.write( "After 10 years, which is 40 quarters, the final balance would be<BR>\n" );
document.write( "$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000%2A1.01%5E40 ALIGN=MIDDLE  ALT=\"10000%2A1.01%5E40\"   DISABLED_style= \"max-width:90%; height:auto;\" > = $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14888.64 ALIGN=MIDDLE  ALT=\"14888.64\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "That's an extra $86.20, due to the interest generated on the interest from the previous quarters. </SPAN>\n" );
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