document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=48083>Question 48083</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I was ableto figure out one of these problems butnot the rest can you help please?\r<BR>\n" );
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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:<BR>\n" );
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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" );
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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" );
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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" );
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document.write( "c) 	Calculate the return (A) if the bank compounds monthly (n = 12). Round your answer to the hundredth's place.<BR>\n" );
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document.write( "d) 	Calculate the return (A) if the bank compounds daily (n = 365). Round your answer to the hundredth's place.<BR>\n" );
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document.write( "e) 	What observation can you make about the size of 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 becomes simpler, that is <BR>\n" );
document.write( " where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding. Round your answer to the hundredth's place.<BR>\n" );
document.write( "Answer:  <BR>\n" );
document.write( "Show work in this space  <BR>\n" );
document.write( "A=Pe^(rt)<BR>\n" );
document.write( "      A = 20000e^(.08*3)<BR>\n" );
document.write( "      A = 20000e^.24<BR>\n" );
document.write( "      A = 20000* 1.27124915<BR>\n" );
document.write( "      A = 25,424.98\r<BR>\n" );
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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). Round your answer to the hundredth's place.<BR>\n" );
document.write( "Answer:  <BR>\n" );
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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? Round your answer to the hundredth's place.<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 #31825 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=31825\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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 <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( "Answer: <BR>\n" );
document.write( "Show work in this space. Use ^ to indicate the power<BR>\n" );
document.write( "<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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+20000%281+%2B+0.08%29%5E%283%29+=+20000%281.08%29%5E3+=+25194.24 ALIGN=MIDDLE  ALT=\"A+=+20000%281+%2B+0.08%29%5E%283%29+=+20000%281.08%29%5E3+=+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). Round your answer to the hundredth's place.<BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "<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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+20000%281+%2B+0.08%2F4%29%5E%284%2A3%29+=+20000%281.02%29%5E12+=+25364.84 ALIGN=MIDDLE  ALT=\"A+=+20000%281+%2B+0.08%2F4%29%5E%284%2A3%29+=+20000%281.02%29%5E12+=+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). Round your answer to the hundredth's place.<BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "<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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+20000%281+%2B+0.08%2F12%29%5E%2812%2A3%29+=+20000%281.00666667%29%5E36+=+25404.74 ALIGN=MIDDLE  ALT=\"A+=+20000%281+%2B+0.08%2F12%29%5E%2812%2A3%29+=+20000%281.00666667%29%5E36+=+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). Round your answer to the hundredth's place.<BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "<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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+20000%281+%2B+0.08%2F365%29%5E%28365%2A3%29+=+20000%281.00021917%29%5E1095+=+25424.31 ALIGN=MIDDLE  ALT=\"A+=+20000%281+%2B+0.08%2F365%29%5E%28365%2A3%29+=+20000%281.00021917%29%5E1095+=+25424.31\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "e) What observation can you make about the size of increase in your return as your compounding increases more frequently?<BR>\n" );
document.write( "n = 1 ~> 25194.24<BR>\n" );
document.write( "n = 4 ~> 25364.84<BR>\n" );
document.write( "n = 12 ~> 25404.74<BR>\n" );
document.write( "n = 365 ~> 25424.31<BR>\n" );
document.write( "As you compound your money more often, you recieve more income from interest. You will acquire more money.<BR>\n" );
document.write( "f) If a bank compounds continuous, then the formula becomes simpler, that is <BR>\n" );
document.write( "where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding. Round your answer to the hundredth's place.<BR>\n" );
document.write( "Answer: <BR>\n" );
document.write( "Show work in this space <BR>\n" );
document.write( "A=Pe^(rt)<BR>\n" );
document.write( "A = 20000e^(.08*3)<BR>\n" );
document.write( "A = 20000e^.24<BR>\n" );
document.write( "A = 20000* 1.27124915<BR>\n" );
document.write( "A = 25,424.98<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). Round your answer to the hundredth's place.<BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "A = Pe^(r*t)<BR>\n" );
document.write( "25000 = 20000e^(0.08*t)<BR>\n" );
document.write( "5/4 = e^(0.08*t)<BR>\n" );
document.write( "ln(1.25) = 0.08t<BR>\n" );
document.write( "ln(1.25)/0.08 = t = 2.79<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? Round your answer to the hundredth's place.<BR>\n" );
document.write( "A = Pe^(r*t)<BR>\n" );
document.write( "2P = Pe^(0.08*t)<BR>\n" );
document.write( "2 = e^(0.08t)<BR>\n" );
document.write( "ln(2) = 0.08t<BR>\n" );
document.write( "ln(2)/0.08 = t = 8.66 </SPAN>\n" );
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