document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151734>Question 1151734</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Susan Orman wants to pay $1,400 semiannually to her granddaughter for 10 years for helping her around the house. If Susan can invest money at 6% compounded quarterly, how much must she invest today to meet this goal? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773560 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52908)</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=773560\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I understand the problem in this way:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "    How much money should Susan deposit today in the morning to pay $1400 semiannually to her granddaughter \r\n" );
document.write( "    for 10 years starting from today at the afternoon for known goal ...\r\n" );
document.write( "\r\n" );
document.write( "     . . . and so on . . . \r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<U>Solution</U>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Use the general formula  X = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%2Ap%2A%28%281-p%5E%28-n%29%29%2Fr%29 ALIGN=MIDDLE  ALT=\"W%2Ap%2A%28%281-p%5E%28-n%29%29%2Fr%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
document.write( "\r\n" );
document.write( "In this case  the withdrawal semi-annual rate is W = $1400,  the semi-annual effective compounding rate \r\n" );
document.write( "is  r = 0.06/2 = 0.03,  p = 1 + 0.03 = 1.03, the number of payment periods  is n = 10*2 = 20. So\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "          X = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1400%2A1.03%2A%28%281-1.03%5E%28-20%29%29%2F0.03%29 ALIGN=MIDDLE  ALT=\"1400%2A1.03%2A%28%281-1.03%5E%28-20%29%29%2F0.03%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 21,453.32 dollars.     <U>ANSWER</U>\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "<U>ANSWER</U>.  To provide her goal, Susan should deposit  $21,453.32 dollars today at this account.\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "\n" );
document.write( "Solved.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "See my lessons in this site associated with annuity saving plans and retirement plans \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Ordinary-Annuity-saving-plans-and-geometric-progressions.lesson>Ordinary Annuity saving plans and geometric progressions</A>\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Annuity-due-saving-plans-and-geometric-progressions.lesson>Annuity Due saving plans and geometric progressions</A>\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Solved-problem-on-Ordinary-Annuity-saving-plans.lesson>Solved problems on Ordinary Annuity saving plans</A> \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Withdrawing-a-certain-amount-of-money-periodically-from-a-compounded-saving-account.lesson>Withdrawing a certain amount of money periodically from a compounded saving account</A> (*)\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Solved-problems-on-Annuity-saving-plans.lesson>Miscellaneous problems on retirement plans</A> \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and especially lesson marked &nbsp;(*) &nbsp;in the list as the most relevant to the given problem.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "These lessons contain all necessary theory, clear explanations and tens of examples.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Happy learning (!)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );