document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=319724>Question 319724</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My question is about an annuity.  How do we solve the annuity formula for time?  Now, scott8148 has been great with reversing a formula with logarithmic conversions, but this seems pretty complex.\r<BR>\n" );
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document.write( "The standard annuity formula reads as such:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=%28P%281%2Br%2Fn%29%5E%28nt-1%29%28r%2Fn%29%29+%2F+%28%281%2Br%2Fn%29%5E%28nt%29-1%29 ALIGN=MIDDLE  ALT=\"w=%28P%281%2Br%2Fn%29%5E%28nt-1%29%28r%2Fn%29%29+%2F+%28%281%2Br%2Fn%29%5E%28nt%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This would answer the question, \"If some money is withdrawn from the principle every month for 20 years, how much could be withdrawn?\"\r<BR>\n" );
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document.write( "Fair enough, but what about a question such as, \"Jan wants to withdraw $800 every month until her account reaches zero.  How long will it be before her account reaches zero?\"  This is assuming that the amount withdrawn would be large enough to break past the interest and cut into the capital, of course.\r<BR>\n" );
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document.write( "Thanks so much for any reply,\r<BR>\n" );
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document.write( "Charlie Bass<BR>\n" );
document.write( "Abilene, TX<BR>\n" );
document.write( "cfbass@yahoo.com </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #229144 by </B><A HREF=/tutors/aboutme.mpl?userid=scott8148><B>scott8148(6628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scott8148><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=scott8148><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=229144\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You again, Charlie?\r<BR>\n" );
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document.write( "multiplying by n/r ___ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=wn%2Fr+=%28P%281%2Br%2Fn%29%5E%28nt-1%29%29+%2F+%28%281%2Br%2Fn%29%5E%28nt%29-1%29 ALIGN=MIDDLE  ALT=\"wn%2Fr+=%28P%281%2Br%2Fn%29%5E%28nt-1%29%29+%2F+%28%281%2Br%2Fn%29%5E%28nt%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "multiplying by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2Br%2Fn%29%5E%28nt%29-1%29 ALIGN=MIDDLE  ALT=\"%28%281%2Br%2Fn%29%5E%28nt%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ___ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%281%2Br%2Fn%29%5E%28nt%29%29%28wn%2Fr%29%29+-+%28wn%2Fr%29+=+%28P%281%2Br%2Fn%29%5E%28nt-1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "subtracting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2Br%2Fn%29%5E%28nt%29%29%28wn%2Fr%29%29 ALIGN=MIDDLE  ALT=\"%28%281%2Br%2Fn%29%5E%28nt%29%29%28wn%2Fr%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ___ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-wn%2Fr+=+%28P%281%2Br%2Fn%29%5E%28nt-1%29%29+-+%28%281%2Br%2Fn%29%5E%28nt%29%29%28wn%2Fr%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "factoring ___ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-wn%2Fr+=+%28%281%2Br%2Fn%29%5E%28nt%29%29+%28%28P%281%2Br%2Fn%29%5E%28-1%29%29+-+%28wn%2Fr%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "dividing by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28P%281%2Br%2Fn%29%5E%28-1%29%29+-+%28wn%2Fr%29%29 ALIGN=MIDDLE  ALT=\"%28%28P%281%2Br%2Fn%29%5E%28-1%29%29+-+%28wn%2Fr%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ___ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-wn%2Fr%29%2F%28%28%28P%281%2Br%2Fn%29%5E%28-1%29%29+-+%28wn%2Fr%29%29%29+=+%28%281%2Br%2Fn%29%5E%28nt%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "taking log ___ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28%28-wn%2Fr%29%2F%28%28%28P%281%2Br%2Fn%29%5E%28-1%29%29+-+%28wn%2Fr%29%29%29%29%29+=+%28nt%29+%28log%28%281%2Br%2Fn%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "dividing by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28log%28%281%2Br%2Fn%29%29%29 ALIGN=MIDDLE  ALT=\"n%28log%28%281%2Br%2Fn%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ___ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28%28-wn%2Fr%29%2F%28%28%28P%281%2Br%2Fn%29%5E%28-1%29%29+-+%28wn%2Fr%29%29%29%29%29%2F%28n+%28log%28%281%2Br%2Fn%29%29%29%29=+t ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "hope this works for you </SPAN>\n" );
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