document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190445>Question 1190445</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A. For all parts of this problem, money is invested in a retirement account with an APR of 8.04%.  (This is close to the average annual return rate for a traditional individual retirement account over the last decade.)  You want to be able to withdraw $24,000 per year for 20 years after retirement.  Round up to the cent for each answer.<BR>\n" );
document.write( "3. How much must you have in the account to start with if compounding and withdrawals are both quarterly?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822141 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=822141\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> for the yearly withdrawals:\r<BR>\n" );
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document.write( "annual payment = 24000 at the beginning of each year, or at the end of each year.<BR>\n" );
document.write( "interest rate = 8.04% per year.<BR>\n" );
document.write( "number of years = 20.<BR>\n" );
document.write( "if the withdrawals are at the beginning of each year, the present value will be equal to 253,824.62.<BR>\n" );
document.write( "if the withdrawals are at the end of each year, the present value will be equal to 234,935.78.\r<BR>\n" );
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document.write( "for the quarterly withdrawals:\r<BR>\n" );
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document.write( "quarterly payment = 24000 / 4 = 6000 at the beginning of each quarter, or at the end of each quarter.<BR>\n" );
document.write( "interest rate = 8.04% each year / 4 = 2.01% per quarter.<BR>\n" );
document.write( "if the withdrawals are at the beginning of each quarter, the present value will be equal to 242,537.94.<BR>\n" );
document.write( "if the withdrawals are at the end of each quarter, the present value will be equal to 237,758.99.\r<BR>\n" );
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document.write( "all input and outputs were rounded to the nearest penny, as instructed.\r<BR>\n" );
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document.write( "it was not given that the withdrawals would be at the end of each time period or at the beginning of each time period, so i gave you both.\r<BR>\n" );
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document.write( "with quarterly compounding, the interest rate per year is divided by 4 and the number of time periods is multiplied by 4.\r<BR>\n" );
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document.write( "let me know if you have any questions.<BR>\n" );
document.write( "theo\r<BR>\n" );
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