document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=332248>Question 332248</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that $2000 is invested at a rate of 6% per year compounded continuously. What is the balance after 1 yr? After 2 yrs? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #238116 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=238116\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Recall that the formula for continuous compounding interest is\r<BR>\n" );
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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;\" >\r<BR>\n" );
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document.write( "where A is the return, P is the principal (amount invested), r is the interest rate (in decimal form) and t is the time in years.\r<BR>\n" );
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document.write( "Since \"$2000 is invested at a rate of 6% per year compounded continuously\", we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=2000 ALIGN=MIDDLE  ALT=\"P=2000\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=0.06 ALIGN=MIDDLE  ALT=\"r=0.06\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the decimal equivalent of 6%).\r<BR>\n" );
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document.write( "Now let's compute the return when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1 ALIGN=MIDDLE  ALT=\"t=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie find the balance after one year)\r<BR>\n" );
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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;\" > Start with the continuous compounding formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2000%2Ae%5E%280.06%2A1%29 ALIGN=MIDDLE  ALT=\"A=2000%2Ae%5E%280.06%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=2000 ALIGN=MIDDLE  ALT=\"P=2000\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=0.06 ALIGN=MIDDLE  ALT=\"r=0.06\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1 ALIGN=MIDDLE  ALT=\"t=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2000%2Ae%5E%280.06%29 ALIGN=MIDDLE  ALT=\"A=2000%2Ae%5E%280.06%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.06 ALIGN=MIDDLE  ALT=\"0.06\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.06 ALIGN=MIDDLE  ALT=\"0.06\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2000%2A1.06183654654536 ALIGN=MIDDLE  ALT=\"A=2000%2A1.06183654654536\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise 'e' (which is approximately 2.71828) to the power <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.06 ALIGN=MIDDLE  ALT=\"0.06\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.06183654654536 ALIGN=MIDDLE  ALT=\"1.06183654654536\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this value is approximate).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2123.67309309072 ALIGN=MIDDLE  ALT=\"A=2123.67309309072\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2000 ALIGN=MIDDLE  ALT=\"2000\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.06183654654536 ALIGN=MIDDLE  ALT=\"1.06183654654536\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2123.67309309072 ALIGN=MIDDLE  ALT=\"2123.67309309072\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2123.67 ALIGN=MIDDLE  ALT=\"A=2123.67\"   DISABLED_style= \"max-width:90%; height:auto;\" > Round to the nearest hundredth (ie to the nearest penny).\r<BR>\n" );
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document.write( "So after 1 year, you'll have about $2,123.67\r<BR>\n" );
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document.write( "Now let's compute the return when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=2 ALIGN=MIDDLE  ALT=\"t=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie find the balance after two years)\r<BR>\n" );
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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;\" > Start with the continuous compounding formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2000%2Ae%5E%280.06%2A2%29 ALIGN=MIDDLE  ALT=\"A=2000%2Ae%5E%280.06%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=2000 ALIGN=MIDDLE  ALT=\"P=2000\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=0.06 ALIGN=MIDDLE  ALT=\"r=0.06\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the decimal equivalent of 6%), and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=2 ALIGN=MIDDLE  ALT=\"t=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2000%2Ae%5E%280.12%29 ALIGN=MIDDLE  ALT=\"A=2000%2Ae%5E%280.12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.06 ALIGN=MIDDLE  ALT=\"0.06\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.12 ALIGN=MIDDLE  ALT=\"0.12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2000%2A1.12749685157938 ALIGN=MIDDLE  ALT=\"A=2000%2A1.12749685157938\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise 'e' (which is approximately 2.71828) to the power <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.12 ALIGN=MIDDLE  ALT=\"0.12\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.12749685157938 ALIGN=MIDDLE  ALT=\"1.12749685157938\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this value is approximate).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2254.99370315875 ALIGN=MIDDLE  ALT=\"A=2254.99370315875\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2000 ALIGN=MIDDLE  ALT=\"2000\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.12749685157938 ALIGN=MIDDLE  ALT=\"1.12749685157938\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2254.99370315875 ALIGN=MIDDLE  ALT=\"2254.99370315875\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2254.99 ALIGN=MIDDLE  ALT=\"A=2254.99\"   DISABLED_style= \"max-width:90%; height:auto;\" > Round to the nearest hundredth (ie to the nearest penny).\r<BR>\n" );
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document.write( "So after two years, you'll have $2,254.99<BR>\n" );
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