document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=34491>Question 34491</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321279085/algebrahomeworkh>COLLEGE ALGEBRA WITH MODELING AND VISUALIZATION</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 3)	The formula for calculating the amount of money returned for an initial deposit money into a bank account or CD (Certificate of Deposit) is given by<BR>\n" );
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document.write( "A is the amount of returned.<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%.<BR>\n" );
document.write( "a)	Calculate the return (A) if the bank compounds annually (n = 1).<BR>\n" );
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document.write( "Show work in this space. Use ^ to indicate the power.	\r<BR>\n" );
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document.write( "b)	Calculate the return (A) if the bank compounds quarterly (n = 4).<BR>\n" );
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document.write( "c)	Calculate the return (A) if the bank compounds monthly (n = 12).<BR>\n" );
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document.write( "d)	Calculate the return (A) if the bank compounds daily (n = 365).<BR>\n" );
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document.write( "e)	What observation can you make about the increase in your return as your compounding increases more frequently? <BR>\n" );
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document.write( "f)	If a bank compounds continuous, then the formula takes a simpler, that is <BR>\n" );
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document.write( "where e is a constant and equals approximately 2.7183.<BR>\n" );
document.write( "Calculate A with continuous compounding. <BR>\n" );
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document.write( "g)	Now suppose, instead of knowing t, we know that the bank returned to us $15,000 with the bank compounding continuously. Using logarithms, find how long we left the money in the bank (find t). <BR>\n" );
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document.write( "h)	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? <BR>\n" );
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document.write( "4)	For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time. Using the formula,  , let r = 10%, P = 1, and n = 1 and give the coordinates (t, A) for the points where t = 0, 1, 2, 3, 4.\r<BR>\n" );
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document.write( "a)	Show coordinates in this space\r<BR>\n" );
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document.write( "b)	Show graph here	\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #20784 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=20784\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do a few of these as examples.<BR>\n" );
document.write( "#b  A=P(1+r/n)^(nt)<BR>\n" );
document.write( "    A=10000(1+0.10/4)^[(4)(2)]<BR>\n" );
document.write( "    A=10000(1+0.025)^8<BR>\n" );
document.write( "    A=10000(1.025)^8<BR>\n" );
document.write( "    A=$12184.03\r<BR>\n" );
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document.write( "#f  A=Pe^(rt)<BR>\n" );
document.write( "    A=10000e^(0.10(2))<BR>\n" );
document.write( "    A=10000e^0.20<BR>\n" );
document.write( "    A=$12214.03\r<BR>\n" );
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document.write( "#g  15000=10000e^(0.10t)<BR>\n" );
document.write( "     1.5 =e^0.10t<BR>\n" );
document.write( "   Take the natural log of both sides to get:<BR>\n" );
document.write( "    ln1.5==0.1t<BR>\n" );
document.write( "   0.40465108...=0.1t<BR>\n" );
document.write( "    t=4.05 years\r<BR>\n" );
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document.write( "#h  20,000=10000e^(0.1t)<BR>\n" );
document.write( "      2=e^0.1t<BR>\n" );
document.write( "   Take the natural log of both sides to get:<BR>\n" );
document.write( "   0.69=0.1t<BR>\n" );
document.write( "    t=6.9 years  (This is called \"the rule of seven\".)<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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