document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1149115>Question 1149115</A>: <I><SPAN STYLE=\"word-break: break-all;\"> We received a lump sum payment of $500,000 that we invested at 7.8% interest, compounded annually.  We plan on withdrawing $40,000 every year.  How long will the money last? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #770476 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=770476\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Learn the basic formulas for annuities and loans, and learn how to do the computations using those formulas; or use any of a number of online calculators....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%28P%281-%281%2Br%29%5E%28-t%29%29%29%2F%28r%29 ALIGN=MIDDLE  ALT=\"A+=+%28P%281-%281%2Br%29%5E%28-t%29%29%29%2F%28r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "A = initial amount<BR>\n" );
document.write( "P = periodic payment (withdrawal)<BR>\n" );
document.write( "r = annual interest rate<BR>\n" );
document.write( "t = number of years<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500000+=+%2840000%281-%281%2B.078%29%5E%28-t%29%29%29%2F%28.078%29 ALIGN=MIDDLE  ALT=\"500000+=+%2840000%281-%281%2B.078%29%5E%28-t%29%29%29%2F%28.078%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28500000%2F40000%29%2A%28.078%29+=+0.975+=+1-%281.078%29%5E%28-t%29 ALIGN=MIDDLE  ALT=\"%28500000%2F40000%29%2A%28.078%29+=+0.975+=+1-%281.078%29%5E%28-t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281.078%29%5E%28-t%29+=+1-0.975+=+0.025 ALIGN=MIDDLE  ALT=\"%281.078%29%5E%28-t%29+=+1-0.975+=+0.025\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2Alog%28%281.078%29%29+=+log%28%280.025%29%29 ALIGN=MIDDLE  ALT=\"-t%2Alog%28%281.078%29%29+=+log%28%280.025%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t+=+log%28%280.025%29%29%2Flog%28%281.078%29%29+=+-49.1 ALIGN=MIDDLE  ALT=\"-t+=+log%28%280.025%29%29%2Flog%28%281.078%29%29+=+-49.1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to 1 decimal place.<br><BR>\n" );
document.write( "ANSWER: 49.11 years<br><BR>\n" );
document.write( "That answer assumes the first withdrawal is at the END of the first year.<br><BR>\n" );
document.write( "With that interpretation, 50 years after the initial investment there will be an amount still in the investment equivalent to approximately one-tenth of $40,000.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );