document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198672>Question 1198672</A>: <I><SPAN STYLE=\"word-break: break-all;\"> With a present value of $140,000, what is the size of the withdrawals that can be made at the end of each quarter for the next 10 years if money is worth 7.5%, compounded quarterly? (Round your answer to the nearest cent.)<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 #833501 by </B><A HREF=/tutors/aboutme.mpl?userid=AbeAlgebraGenius><B>AbeAlgebraGenius(2)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AbeAlgebraGenius><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=833501\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For this problem, we need to use the Present Value of Ordinary Annuity formula.\r<BR>\n" );
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document.write( "W = B(r/n) / [ 1 - (1 + r/n)^-nt ].\r<BR>\n" );
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document.write( "W = Withdrawal amount every period (quarter).<BR>\n" );
document.write( "B = Original balance in the account.<BR>\n" );
document.write( "r = Annual interest rate.<BR>\n" );
document.write( "n = Number of times interest is compounded per year<BR>\n" );
document.write( "  = Number of times withdrawals are made per year.<BR>\n" );
document.write( "t = Number of years withdrawals are made.\r<BR>\n" );
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document.write( "In our case we have:  B = 140,000 (original balance)<BR>\n" );
document.write( "                      r = 0.075   (7.5% interest rate)<BR>\n" );
document.write( "                      n = 4       (four quarters per year)<BR>\n" );
document.write( "                      t = 10      (total of 10 years of withdrawals).\r<BR>\n" );
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document.write( "W = 140000 (0.075/4) / [1 - (1 + 0.075/4)^-40]<BR>\n" );
document.write( "  = 140000 (0.01875) / [1 - (1 + 0.01875)^-40]<BR>\n" );
document.write( "  = 2625 / (1 - 1.01875^-40)<BR>\n" );
document.write( "  = 2625 / (1 - 0.475658356)<BR>\n" );
document.write( "  = 2625 / 0.524341645<BR>\n" );
document.write( "  = 5006.28\r<BR>\n" );
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document.write( "Thus, the size of withdrawals each quarter is $5,006.28; for the next 10 years. </SPAN>\n" );
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