document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=256355>Question 256355</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i'm doing business algebra online in college, and we're now talking about continuous compound interest.  The formula i'm struggling with is the Pert formula.  I'm stuck on how to solve a problem when i know what the P, r and t is, but what is the e for?  I've never figured out how to come up with the same answer as my study guide example.\r<BR>\n" );
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document.write( "For example:  Use the continuous compound interest formula to find the indicated value.  A=$7,700; r=8.78%; t=10 years; P=?  P=_______(round to two decimal places as needed).\r<BR>\n" );
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document.write( "I look forward to getting a reply back soon.  Hopefully I will get this figured out soon.  Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #188489 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=188489\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> with continuous compounding formula, you get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+=+p+%2A+e%5Ert ALIGN=MIDDLE  ALT=\"f+=+p+%2A+e%5Ert\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "f = future value<BR>\n" );
document.write( "p = present amount<BR>\n" );
document.write( "r = annual interest rate<BR>\n" );
document.write( "t = number of years\r<BR>\n" );
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document.write( "the e is the symbol for the scientific constant of 2.718281828...\r<BR>\n" );
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document.write( "This is an irrational number (never ending non repeating fractional part).\r<BR>\n" );
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document.write( "It's called Napier's constant.\r<BR>\n" );
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document.write( "the formula for the base of e to an exponent is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex ALIGN=MIDDLE  ALT=\"e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > where x is the exponent.\r<BR>\n" );
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document.write( "the inverse formula of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex ALIGN=MIDDLE  ALT=\"e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%29 ALIGN=MIDDLE  ALT=\"ln%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means the natural log of x.\r<BR>\n" );
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document.write( "the basis definition of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex ALIGN=MIDDLE  ALT=\"e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+e%5Ex ALIGN=MIDDLE  ALT=\"y+=+e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+ln%28y%29 ALIGN=MIDDLE  ALT=\"x+=+ln%28y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "this is nothing more than your normal logarithm functions except you have a base of e.\r<BR>\n" );
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document.write( "It's no different than the statement:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+10%5Ex ALIGN=MIDDLE  ALT=\"y+=+10%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2Cx%29+=+y ALIGN=MIDDLE  ALT=\"log%2810%2Cx%29+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "let x = 3\r<BR>\n" );
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document.write( "{y = 10^3}}} = 10*10*10 = 1000\r<BR>\n" );
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document.write( "the statement becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+10%5E3 ALIGN=MIDDLE  ALT=\"y+=+10%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C1000%29+=+3 ALIGN=MIDDLE  ALT=\"log%2810%2C1000%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "you can confirm that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C1000%29+=+3 ALIGN=MIDDLE  ALT=\"log%2810%2C1000%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > by using your calculator and taking the log of 3.   \r<BR>\n" );
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document.write( "you will get 1000.\r<BR>\n" );
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document.write( "the base e is nothing more than another base to work with.\r<BR>\n" );
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document.write( "In your problem, here's how you would work it.\r<BR>\n" );
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document.write( "formula is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+=+p+%2A+e%5Ert ALIGN=MIDDLE  ALT=\"f+=+p+%2A+e%5Ert\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "you are given:\r<BR>\n" );
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document.write( "p = $7,700<BR>\n" );
document.write( "r = 8.78%<BR>\n" );
document.write( "t = 10 years\r<BR>\n" );
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document.write( "first thing you need to do is take all the dollar signs and commas out of p to get:\r<BR>\n" );
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document.write( "p = 7700\r<BR>\n" );
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document.write( "next thing you need to do is divide 8.78% by 100% to get .0878.\r<BR>\n" );
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document.write( "in the formula, you need to work with the rate, not the percent.\r<BR>\n" );
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document.write( "since r is an innual interest rate already, you do not need to adjust it any further.\r<BR>\n" );
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document.write( "since t is already specified in years, you do not need to adjust it any further.\r<BR>\n" );
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document.write( "plug these values into your formula to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+=+p+%2A+e%5Ert ALIGN=MIDDLE  ALT=\"f+=+p+%2A+e%5Ert\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+=+7700+%2A+e%5E%28.0878%2A10%29 ALIGN=MIDDLE  ALT=\"f+=+7700+%2A+e%5E%28.0878%2A10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+=+7700+%2A+e%5E%28.878%29 ALIGN=MIDDLE  ALT=\"f+=+7700+%2A+e%5E%28.878%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "use your calculator to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28.878%29 ALIGN=MIDDLE  ALT=\"e%5E%28.878%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2.406082726\r<BR>\n" );
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document.write( "alternatively, you can substitute the constant of 2.718281828 to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.718281828%5E%28.878%29+=+2.406082725.%0D%0A%0D%0A%0D%0AIt%27s+a+little+off+from+what+the+calculater+would+give+you+but+it%27s+very+close.+++That%27s+beceuase+of+some+rounding+going+on+when+you+see+the+display+of+the+number.+++The+internally+stored+number+is+accurate+to+more+decimal+places.%0D%0A%0D%0A%0D%0Ayour+equation+becomes%3A%0D%0A%0D%0A%0D%0A%7B%7B%7Bf+=+7700+%2A+2.406082726 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solve for f to get:\r<BR>\n" );
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document.write( "f = 18526.83699\r<BR>\n" );
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document.write( "that's equivalent to $18,526.84.\r<BR>\n" );
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document.write( "for some good examples of continuous compounding, check out the web.\r<BR>\n" );
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document.write( "do a search on \"continuous compounding\".\r<BR>\n" );
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document.write( "one such website is <a  rel=nofollow HREF= \"http://moneychimp.com/articles/finworks/continuous_compounding.htm\" target = \"_blank\">http://moneychimp.com/articles/finworks/continuous_compounding.htm</a>\r<BR>\n" );
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document.write( "It has a calculator that lets you calculate different numbers and see the effect of continuous compounding compared to discrete compounding such as yearly, monthly, daily, and hourly.\r<BR>\n" );
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document.write( "It also has a box where you can put in the number of time periods you want.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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