document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=971373>Question 971373</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How much should you invest in a continuously compounded account at an annually interest rate of 6% if you want exactly $8000 after four years? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #854515 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(53875)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=854515\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "How much should you invest in a continuously compounded account at an annually interest rate of 6% <BR>\n" );
document.write( "if you want exactly $8000 after four years?<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Calculations in the post by @lwsshak3 are incorrect.\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I came to provide an accurate solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Formula for a continuous compounding account: A=Pe^rt, <BR>\n" );
document.write( "P = initial investment, <BR>\n" );
document.write( "r = interest rate, <BR>\n" );
document.write( "t=years, <BR>\n" );
document.write( "A=amt after t-yrs\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For given problem:<BR>\n" );
document.write( "r = 0.06<BR>\n" );
document.write( "t = 4<BR>\n" );
document.write( "A = 8000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "..\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "P = A/e^rt = 8000/e^(0.06*4) = 8000/e^(0.24)= 6293.02.\r<BR>\n" );
document.write( "\n" );
document.write( "How much should you invest in the continuously compounded account? $6293.02.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solved correctly.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );