document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=556128>Question 556128</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a few similar questions, so I preferred submitting them in a single question rather than in a different one. I hope that is alright.\r<BR>\n" );
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document.write( "1. What annual rate compounded continuously is equivalent to an effective rate of 5%?\r<BR>\n" );
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document.write( "2. What annual rate r compounded continuously is equivalent to a nominal rate if 6% compounded semi-annually?\r<BR>\n" );
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document.write( "3. If interest is compounded continuously at an annual rate of 0.07, how many years would it take for a principal P o triple? Give your answer to the nearest year.\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 #362103 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=362103\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. What annual rate compounded continuously is equivalent to an effective rate of 5%?<BR>\n" );
document.write( "Continuous interest formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+P%2Ae%5E%28rt%29 ALIGN=MIDDLE  ALT=\"A+=+P%2Ae%5E%28rt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for 1 yr: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+P%2Ae%5Er ALIGN=MIDDLE  ALT=\"A+=+P%2Ae%5Er\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simple interest formula for 1 yr: A = P*(1+r)<BR>\n" );
document.write( "A simple equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Er ALIGN=MIDDLE  ALT=\"e%5Er\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.05<BR>\n" );
document.write( "Find the nat log of both sides (nat log of e = 1)<BR>\n" );
document.write( "r = ln(1.05)<BR>\n" );
document.write( "r = .04879 ~ 4.88% cont interest is equiv to 5% simple int for 1 yr<BR>\n" );
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document.write( "2. What annual rate r compounded continuously is equivalent to a nominal rate if 6% compounded semi-annually?<BR>\n" );
document.write( "Compounded semi annually: (1.03)^2 = 1.0609 <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Er ALIGN=MIDDLE  ALT=\"e%5Er\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.0609<BR>\n" );
document.write( "r = ln(1.0609)<BR>\n" );
document.write( "r = .0591 ~ 5.91% cont interest<BR>\n" );
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document.write( "3. If interest is compounded continuously at an annual rate of 0.07, how many years would it take for a principal P to triple? <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28.07t%29 ALIGN=MIDDLE  ALT=\"e%5E%28.07t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3<BR>\n" );
document.write( ".07t = ln(3)<BR>\n" );
document.write( ".07t = 1.0986<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0986%2F.07 ALIGN=MIDDLE  ALT=\"1.0986%2F.07\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 15.7 ~ 16 yrs to triple </SPAN>\n" );
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