document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=125490>Question 125490</A>: <I><SPAN STYLE=\"word-break: break-all;\"> These questions have really got me stumped!  I dont understand some problems sometimes, and these are a few of them, they all use the following formula to solve it.  Thank you so much, Have a blessed day!!\r<BR>\n" );
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document.write( "The formula for calculating the amount of money returned for an initial deposit into a bank account or CD (certificate of deposit) is given by<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=P%281%2Br%2Fn%29%5Ent ALIGN=MIDDLE  ALT=\"A=P%281%2Br%2Fn%29%5Ent\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "A is the amount of the return.<BR>\n" );
document.write( "P is the principal amount initially deposited.<BR>\n" );
document.write( "r is the annual interest rate (expressed as a decimal).<BR>\n" );
document.write( "n is the number of compound periods in one year.<BR>\n" );
document.write( "t is the number of years.\r<BR>\n" );
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document.write( "Carry all calculations to six decimals on each intermediate step, then round the final answer to the nearest cent.<BR>\n" );
document.write( "Suppose you deposit $2,000 for 5 years at a rate of 8%.\r<BR>\n" );
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document.write( "a) Calculate the return (A) if the bank compounds annually (n = 1). Round your answer to the hundredth's place.\r<BR>\n" );
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document.write( "b) Calculate the return (A) if the bank compounds quarterly (n = 4).  Round your answer to the hundredth's place.<BR>\n" );
document.write( "c) Does compounding annually or quarterly yield more interest?  Explain why<BR>\n" );
document.write( "d) If a bank compounds continuously, then the formula used is  <BR>\n" );
document.write( "where e is a constant and equals approximately 2.7183.<BR>\n" );
document.write( "Calculate A with continuous compounding. Round your answer to the hundredth's place.<BR>\n" );
document.write( "e) A commonly asked question is, “How long will it take to double my money?” At 8% interest rate and continuous compounding, what is the answer? Round your answer to the hundredth's place. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #91960 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=91960\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Parts a and b of your problem are just plugging in numbers and doing the arithmetic.  For a, put 1 in for n, 5 in for t, and convert 8% to a decimal, namely 0.08, and put that in for r.\r<BR>\n" );
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document.write( "For b, same thing, except you put in 4 for n.\r<BR>\n" );
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document.write( "You can punch numbers on a calculator as well as I can so I'll leave that part to you.\r<BR>\n" );
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document.write( "Part c asks about the difference between compounding annually or quarterly.  Let's look at an example.  Say you had $1000 in the bank at 4% for one year.<BR>\n" );
document.write( "At the end of a year of annual compounding, you would have $1040, or a $40 yield.  But if it was quarterly compounding, at the end of the first quarter, they would pay 1% or $10, so you would have $1010.  At the end of the second quarter you would receive another 1% interest, but paid against the new $1010 balance, so you would get an interest payment of $10.10 making your balance $1020.10.  The next quarter your interest payment would be $10.201 and the balance would be $1030.301, and the last quarter, you would get $10.303, for a balance of $1040.602, or $.60 better than you did compounding annually.  In general, the more frequently you compound, the greater the yield for a given rate of annual interest -- that's because you are being paid interest on interest already earned.\r<BR>\n" );
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document.write( "Part d.  You left off the formula, but it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=Pe%5E%28rt%29 ALIGN=MIDDLE  ALT=\"A=Pe%5E%28rt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Just remember the word PERT.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=rt=.04%2A5=0.2 ALIGN=MIDDLE  ALT=\"rt=.04%2A5=0.2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  If you use the calculator built in to Windows, turn on the scientific mode, click the INV checkbox, click the 1 key, click the ln function key, (you should have the value for e - 2.7183...), multiply, 0.2,multiply,2000.  You should get roughly $2442.81\r<BR>\n" );
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document.write( "Part e.  \r<BR>\n" );
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document.write( "Start with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=Pe%5E%28rt%29 ALIGN=MIDDLE  ALT=\"A=Pe%5E%28rt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We want to solve for t when A = 2P, so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28e%2C2%29=log%28e%2Ce%5E%28rt%29%29 ALIGN=MIDDLE  ALT=\"log%28e%2C2%29=log%28e%2Ce%5E%28rt%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28e%2C2%29=rt%2Alog%28e%2Ce%29 ALIGN=MIDDLE  ALT=\"log%28e%2C2%29=rt%2Alog%28e%2Ce%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28e%2Ce%29=1 ALIGN=MIDDLE  ALT=\"log%28e%2Ce%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so\r<BR>\n" );
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document.write( "and finally <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=log%28e%2C2%29%2Fr ALIGN=MIDDLE  ALT=\"t=log%28e%2C2%29%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For a rate of 8%, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=log%28e%2C2%29%2F.08 ALIGN=MIDDLE  ALT=\"t=log%28e%2C2%29%2F.08\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "On the Windows calculator, press 2, press the ln (ln means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28e%2Cx%29 ALIGN=MIDDLE  ALT=\"log%28e%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)function key, divide, .08, equals roughly 8.66.\r<BR>\n" );
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document.write( "There is a quick way to approximate the time it takes for money to double.  You divide 72 by the interest rate as a whole number.  In this case 72/8 = 9 -- way close enough if you need to do the calculation quickly in your head. </SPAN>\n" );
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