document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=111899>Question 111899</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am not sure how to set up and solve the formula for compound interest. I have the formula but not sure what goes where and the steps to solve this question.\r<BR>\n" );
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document.write( "Lee opened a retirement account with an initial investment of $10,000 at an annual interest rate of 8.5%. If the interest is compounded daily, how much will be in the account at the end of 25 years?<BR>\n" );
document.write( "A=10,000 ?<BR>\n" );
document.write( "P=?<BR>\n" );
document.write( "r=8.5% ?<BR>\n" );
document.write( "x=?<BR>\n" );
document.write( "n=25 years ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #81642 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=81642\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a straight-forward compound interest problem. No matter what the numbers are, it works like this.\r<BR>\n" );
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document.write( "You are starting with $10,000 and the ANNUAL interest rate is 8.5%, but you are compounding daily.  There are 365 days in a year (give or take) so at the end of the first day, you will have your initial investment plus one 365th of the annual interest.  You can write it like this: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000%2A%281%2B%28.085%2F365%29%29 ALIGN=MIDDLE  ALT=\"10000%2A%281%2B%28.085%2F365%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The expression in the parentheses consists of 1 which gives you the amount of your initial investment plus the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.085%2F365 ALIGN=MIDDLE  ALT=\".085%2F365\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is the interest that you earned for that day.\r<BR>\n" );
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document.write( "At the end of the second day, you will have what you had at the end of the first day times that same expression again:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000%2A%281%2B%28.085%2F365%29%29%2A%281%2B%28.085%2F365%29%29 ALIGN=MIDDLE  ALT=\"10000%2A%281%2B%28.085%2F365%29%29%2A%281%2B%28.085%2F365%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but you can also write this as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000%2A%281%2B%28.085%2F365%29%29%5E2 ALIGN=MIDDLE  ALT=\"10000%2A%281%2B%28.085%2F365%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the exponent being the number of days that have elapsed so far.\r<BR>\n" );
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document.write( "But you have a 25 year investment, so you need to know the number of days in 25 years, or 25 * 365 = 9125.\r<BR>\n" );
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document.write( "So, your complete expression is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000%2A%281%2B%28.085%2F365%29%29%5E9125 ALIGN=MIDDLE  ALT=\"10000%2A%281%2B%28.085%2F365%29%29%5E9125\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  You need a REALLY good calculator, or use MS Excel.  Just type the following into a cell on a blank Excel worksheet and you will get your answer: =10000*(1+(0.085/365))^9125\r<BR>\n" );
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document.write( "By the way, if you wanted to get really precise and use 365.25 as the number of days in a year, the answer comes out about $0.015 different.  Or if you want to use the common financial institution practice of counting 360 days per year, the difference is about $0.29.  In other words, don't sweat the small stuff.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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