document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187955>Question 1187955</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 19.	Karen has been depositing RM300 at the end of each month in a tax-free retirement account since she was 25. Louis, who is the same age as Karen, started depositing RM420 at the end of each month in a tax-free retirement account when he was 30. Assuming that both accounts have been and will be earning interest at the rate of 5.4%/year compounded monthly, who will end up with the larger retirement account at the age of 60, Karen or Loius? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818974 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=818974\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the calculator at <a  rel=nofollow HREF= \"https://arachnoid.com/finance/index.html\" target = \"_blank\">https://arachnoid.com/finance/index.html</a> tells you what the future value is, as shown below:\r<BR>\n" );
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document.write( "inputs are everything but fv.<BR>\n" );
document.write( "output is fv.\r<BR>\n" );
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document.write( "the calculator tells you that the 300 a month plan gives a future value of 372,757.56 at the end of 420 months, while the 420 a month plan gives a future value of 376,577.62 at the end of 360 months.\r<BR>\n" );
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document.write( "since karen has the 300 a month plan and louis has the 420 a month plan, louis winds up with more money at the end of 30 years than karen has at the end of 35 years.\r<BR>\n" );
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document.write( "that would be your solution.\r<BR>\n" );
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document.write( "that same calculator tells you when both plans have the same future value.\r<BR>\n" );
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document.write( "the calculator says that the remaining balance for the 420 a month plan will be equal to the remaining balance for the 300 a month at the end of month 330.95 for the 420 a month plan, which corresponds to end of month 391 for the 300 a month plan.\r<BR>\n" );
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document.write( "i used excel to track the monthly remaining balances.<BR>\n" );
document.write( "excel shows that the 420 a month plan overtakes the 300 a month plan at end of month 331 for the 420 a month plan, which corresponds to month 391 for the 300 a month plan.\r<BR>\n" );
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document.write( "since the 420 a month plan started 60 months later, end of month 391 for the 300 a month plan is the same time frame as end of month 331 for the 420 a month plan.\r<BR>\n" );
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document.write( "here are the significant time points for both plans.\r<BR>\n" );
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document.write( "the display shows that the 420 a month plan overtakes the 300 a month plan in month 331 for the 420 a month plan, which corresponds to month 391 for the 300 a month plan.\r<BR>\n" );
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document.write( "the column heading in the excel display mean:\r<BR>\n" );
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document.write( "nyrs = number of years<BR>\n" );
document.write( "nym = number of months<BR>\n" );
document.write( "rpy = interest rate per year (equal to % divided by 100).<BR>\n" );
document.write( "rpm = interest rate per month<BR>\n" );
document.write( "paeom = payment at the end of each month\r<BR>\n" );
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document.write( "eom = end of month<BR>\n" );
document.write( "rembal = remaining balance at the end of each month.\r<BR>\n" );
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document.write( "let me know if you have any questions.\r<BR>\n" );
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document.write( "theo<BR>\n" );
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