document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=38411>Question 38411</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Need help answering this question please.  Have to have it done by tonight.<BR>\n" );
document.write( "3)	The formula for calculating the amount of money returned for deposit money into a bank account or CD (Certificate of Deposit) is given by the following:\r<BR>\n" );
document.write( "\n" );
document.write( "A = P(1+ r over n)^nt<BR>\n" );
document.write( " <BR>\n" );
document.write( "A is the amount of returned<BR>\n" );
document.write( "P is the principal amount 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" );
document.write( "\n" );
document.write( "Suppose you deposit $20,000 for 3 years at a rate of 8%.<BR>\n" );
document.write( "a)	Calculate the return (A) if the bank compounds annually (n = 1).<BR>\n" );
document.write( "Answer:  <BR>\n" );
document.write( "Show work in this space. Use ^ to indicate the power.  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b)	Calculate the return (A) if the bank compounds quarterly (n = 4), and carry all calculations to 7 significant figures.<BR>\n" );
document.write( "Answer:  <BR>\n" );
document.write( "Show work in this space .  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c)	Calculate the return (A) if the bank compounds monthly (n = 12), and carry all calculations to 7 significant figures.<BR>\n" );
document.write( "Answer:  <BR>\n" );
document.write( "Show work in this space.   \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "d)	Calculate the return (A) if the bank compounds daily (n = 365), and carry all calculations to 7 significant figures.<BR>\n" );
document.write( "Answer:  <BR>\n" );
document.write( "Show work in this space.  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "e)	What observation can you make about the increase in your return as your compounding increases more frequently? <BR>\n" );
document.write( "Answer:  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f)	If a bank compounds continuous, then the formula becomes simpler, that is A=Pe^rt<BR>\n" );
document.write( " where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding. <BR>\n" );
document.write( "Answer:  <BR>\n" );
document.write( "Show work in this space  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "g)	Now suppose, instead of knowing t, we know that the bank returned to us $25,000 with the bank compounding continuously. Using logarithms, find how long we left the money in the bank (find t). <BR>\n" );
document.write( "Answer:  <BR>\n" );
document.write( "Show work in this space  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "h)	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? <BR>\n" );
document.write( "Answer:  Show work in this space.<BR>\n" );
document.write( "  \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #23911 by </B><A HREF=/tutors/aboutme.mpl?userid=Nate><B>Nate(3500)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Nate><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=23911\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+P%281%2B+r%2Fn%29%5E%28nt%29 ALIGN=MIDDLE  ALT=\"A+=+P%281%2B+r%2Fn%29%5E%28nt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Suppose you deposit $20,000 for 3 years at a rate of 8%.<BR>\n" );
document.write( "a) Calculate the return (A) if the bank compounds annually (n = 1).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+20000%281%2B+.08%2F1%29%5E%281%2A3%29 ALIGN=MIDDLE  ALT=\"A+=+20000%281%2B+.08%2F1%29%5E%281%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+20000%281.08%29%5E%283%29 ALIGN=MIDDLE  ALT=\"A+=+20000%281.08%29%5E%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+25194.24 ALIGN=MIDDLE  ALT=\"A+=+25194.24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b) Calculate the return (A) if the bank compounds quarterly (n = 4)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+20000%281%2B+.08%2F4%29%5E%284%2A3%29 ALIGN=MIDDLE  ALT=\"A+=+20000%281%2B+.08%2F4%29%5E%284%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+20000%281.02%29%5E%2812%29 ALIGN=MIDDLE  ALT=\"A+=+20000%281.02%29%5E%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+25364.84 ALIGN=MIDDLE  ALT=\"A+=+25364.84\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c) Calculate the return (A) if the bank compounds monthly (n = 12)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+20000%281%2B+.08%2F12%29%5E%2812%2A3%29 ALIGN=MIDDLE  ALT=\"A+=+20000%281%2B+.08%2F12%29%5E%2812%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+20000%281%2B+.08%2F12%29%5E%2836%29 ALIGN=MIDDLE  ALT=\"A+=+20000%281%2B+.08%2F12%29%5E%2836%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+25404.74 ALIGN=MIDDLE  ALT=\"A+=+25404.74\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d) Calculate the return (A) if the bank compounds daily (n = 365)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+20000%281%2B+.08%2F365%29%5E%28365%2A3%29 ALIGN=MIDDLE  ALT=\"A+=+20000%281%2B+.08%2F365%29%5E%28365%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+20000%281%2B+.08%2F365%29%5E%281095%29 ALIGN=MIDDLE  ALT=\"A+=+20000%281%2B+.08%2F365%29%5E%281095%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+25424.31 ALIGN=MIDDLE  ALT=\"A+=+25424.31\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "e) As the time or interest or frequency of compounded times increases, the amount of total money will increase.<BR>\n" );
document.write( "f) If a bank compounds continuous, then the formula becomes simpler, that 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;\" ><BR>\n" );
document.write( " where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%2820000%29e%5E%28.08%2A3%29 ALIGN=MIDDLE  ALT=\"A=%2820000%29e%5E%28.08%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=25424.98 ALIGN=MIDDLE  ALT=\"A=25424.98\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "g) Now suppose, instead of knowing t, we know that the bank returned to us $25,000 with the bank compounding continuously. Using logarithms, find how long we left the money in the bank (find t). <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25000=20000e%5E%28.08t%29 ALIGN=MIDDLE  ALT=\"25000=20000e%5E%28.08t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F4%29=e%5E%28.08t%29 ALIGN=MIDDLE  ALT=\"%285%2F4%29=e%5E%28.08t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%285%2F4%29=.08t ALIGN=MIDDLE  ALT=\"ln%285%2F4%29=.08t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%285%2F4%29%2F.08=t ALIGN=MIDDLE  ALT=\"ln%285%2F4%29%2F.08=t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In about 2.789294<BR>\n" );
document.write( "h) 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? <BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40000=20000e%5E%28.08t%29 ALIGN=MIDDLE  ALT=\"40000=20000e%5E%28.08t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=e%5E%28.08t%29 ALIGN=MIDDLE  ALT=\"2=e%5E%28.08t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%282%29=.08t ALIGN=MIDDLE  ALT=\"ln%282%29=.08t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%282%29%2F.08=t ALIGN=MIDDLE  ALT=\"ln%282%29%2F.08=t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In about 8.664340 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );