document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=43603>Question 43603</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ok, I've got a real big problem here and i'm thoroughly overwhelmed and confused.  Can someone please help.  Here's the problem:\r<BR>\n" );
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document.write( "The formula for calculating the amount of money returned for an initial deposit money into a back account or CD (Certificate of Deposit) is given by<BR>\n" );
document.write( "A = P(1 + r/n)^m.\r<BR>\n" );
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document.write( "A is the amount of 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 compound period<BR>\n" );
document.write( "T is the number of years\r<BR>\n" );
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document.write( "Suppose you deposit $10,000 for 2 years at a rate of 10%.  Calculate the return (A) if the bank compounds annual (n=1).<BR>\n" );
document.write( "Answer -\r<BR>\n" );
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document.write( "Show work in space.  Use ^ to indicate the power.\r<BR>\n" );
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document.write( "Calculate the return (A) if the bank compounds quarterly (n = 4), and carry all calculations to 7 significant figures.\r<BR>\n" );
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document.write( "Answer -\r<BR>\n" );
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document.write( "Show work in this space - \r<BR>\n" );
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document.write( "Calculate the return (A) if the bank compounds monthly (n=12), and carry all calculations to 7 significant figures.\r<BR>\n" );
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document.write( "Answer -\r<BR>\n" );
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document.write( "Show work in space -\r<BR>\n" );
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document.write( "Calculate the return (A) if the bank compounds daily (n=365), and carry all calculations to 7 significant figures.\r<BR>\n" );
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document.write( "Answer -\r<BR>\n" );
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document.write( "Show work in space -\r<BR>\n" );
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document.write( "What observation can you make about the increase in your return as your compounding increases more frequently?\r<BR>\n" );
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document.write( "Answer -\r<BR>\n" );
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document.write( "If a bank compounds continuously, then the formula takes a simpler, that is A = Pe^n.  Where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding.\r<BR>\n" );
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document.write( "Answer -\r<BR>\n" );
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document.write( "Show work in space -\r<BR>\n" );
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document.write( "Now suppose, instead of knowing t, we know that the bank returned to us $15,000 with the bank compounding continuously.  Using natural logarithms, find how long we left the money in the bank (find f).\r<BR>\n" );
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document.write( "Answer -\r<BR>\n" );
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document.write( "Show work in space - \r<BR>\n" );
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document.write( "A commonly asked question is, \"How long will it take to double my money?\" At 10% interest rate and continuous compounding, what is the answer?\r<BR>\n" );
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document.write( "Answer - \r<BR>\n" );
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document.write( "Show work in space -  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #28609 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=28609\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A = P(1 + r/n)^m.\r<BR>\n" );
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document.write( "Suppose you deposit $10,000 for 2 years at a rate of 10%.  Calculate the return (A) if the bank compounds annual (n=1).\r<BR>\n" );
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document.write( "A=10000(1+0.10/1)^2<BR>\n" );
document.write( "A=10000*1.21= 12100\r<BR>\n" );
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document.write( "Calculate the return (A) if the bank compounds quarterly (n = 4), and carry all calculations to 7 significant figures. (I assume you mean for 2 years)<BR>\n" );
document.write( "A=10000(1+0.10/4)^(4*2)<BR>\n" );
document.write( "A=10000(1.2184029<BR>\n" );
document.write( "A=12184.03\r<BR>\n" );
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document.write( "Calculate the return (A) if the bank compounds monthly (n=12), and carry all calculations to 7 significant figures. (I assume you for 2 years) <BR>\n" );
document.write( "A=10000(1+0.10/12)^(12*2)<BR>\n" );
document.write( "Use your caluculator.\r<BR>\n" );
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document.write( "Calculate the return (A) if the bank compounds daily (n=365), and carry all calculations to 7 significant figures. (I assume you mean for two years)\r<BR>\n" );
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document.write( "A=10000(1+0.10/365)^(365*2)<BR>\n" );
document.write( "Use calculator.\r<BR>\n" );
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document.write( "What observation can you make about the increase in your return as your compounding increases more frequently?<BR>\n" );
document.write( "That should be obvious.\r<BR>\n" );
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document.write( "If a bank compounds continuously, then the formula takes a simpler, that is A = Pe^n.  Where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding.<BR>\n" );
document.write( "You have to be given the rate and the number of years.\r<BR>\n" );
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document.write( "A=Pe^(rn)<BR>\n" );
document.write( "A=10000(e^(0.10*?)\r<BR>\n" );
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document.write( "Now suppose, instead of knowing t, we know that the bank returned to us $15,000 with the bank compounding continuously.  Using natural logarithms, find how long we left the money in the bank (find f).\r<BR>\n" );
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document.write( "15000=10000e^(0.10t)<BR>\n" );
document.write( "1.5=e^0.10t<BR>\n" );
document.write( "ln(1.5)=0.10t<BR>\n" );
document.write( "0.40546511...=0.10t<BR>\n" );
document.write( "t=4.05 years\r<BR>\n" );
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document.write( "\"How long will it take to double my money?\" At 10% interest rate and continuous compounding\r<BR>\n" );
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document.write( "2P=Pe^(0.10t)<BR>\n" );
document.write( "2=e^(0.10t)<BR>\n" );
document.write( "ln2=0.10t<BR>\n" );
document.write( "0.69314718...=0.10t<BR>\n" );
document.write( "t=6.93 years<BR>\n" );
document.write( "This is generally call \"the rule of seven\".\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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