document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179080>Question 1179080</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Grandma decides to put 1300 dollars every month into an account for you. She makes 23 monthly deposits, the last coming September 1, 2003 - the day you start college. She wants you to be able to withdraw money from this account at the beginning of each month, with the first withdrawal coming September 1, 2003 and the last coming June 1, 2008, (when you'll graduate). (Note: that makes 58 withdrawals total.) How much will you be able to withdraw each month if the account is earning a nominal interest rate of 9.3 percent convertible monthly? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850266 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850266\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break this problem into two parts:\r<BR>\n" );
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document.write( "**Part 1: Calculate the Accumulated Value of Grandma's Deposits**\r<BR>\n" );
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document.write( "1.  **Monthly Deposit:** $1300<BR>\n" );
document.write( "2.  **Number of Deposits:** 23<BR>\n" );
document.write( "3.  **Interest Rate:** 9.3% convertible monthly (0.093 / 12 = 0.00775 per month)\r<BR>\n" );
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document.write( "We'll use the future value of an ordinary annuity formula:\r<BR>\n" );
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document.write( "FV = P * [((1 + r)^n - 1) / r]\r<BR>\n" );
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document.write( "Where:\r<BR>\n" );
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document.write( "* FV = Future Value<BR>\n" );
document.write( "* P = Periodic Payment ($1300)<BR>\n" );
document.write( "* r = Interest Rate per Period (0.00775)<BR>\n" );
document.write( "* n = Number of Periods (23)\r<BR>\n" );
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document.write( "FV = 1300 * [((1 + 0.00775)^23 - 1) / 0.00775]<BR>\n" );
document.write( "FV = 1300 * [(1.00775^23 - 1) / 0.00775]<BR>\n" );
document.write( "FV = 1300 * [(1.196398246 - 1) / 0.00775]<BR>\n" );
document.write( "FV = 1300 * [0.196398246 / 0.00775]<BR>\n" );
document.write( "FV = 1300 * 25.3416<BR>\n" );
document.write( "FV ≈ $32944.08\r<BR>\n" );
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document.write( "**Part 2: Calculate the Monthly Withdrawal Amount**\r<BR>\n" );
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document.write( "1.  **Accumulated Value (Present Value for Withdrawals):** $32944.08<BR>\n" );
document.write( "2.  **Number of Withdrawals:** 58<BR>\n" );
document.write( "3.  **Interest Rate:** 9.3% convertible monthly (0.093 / 12 = 0.00775 per month)\r<BR>\n" );
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document.write( "We'll use the present value of an annuity due formula since withdrawals are at the beginning of each month:\r<BR>\n" );
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document.write( "PV = M * [(1 - (1 + r)^-n) / r] * (1 + r)\r<BR>\n" );
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document.write( "Where:\r<BR>\n" );
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document.write( "* PV = Present Value ($32944.08)<BR>\n" );
document.write( "* M = Monthly Withdrawal Amount<BR>\n" );
document.write( "* r = Interest Rate per Period (0.00775)<BR>\n" );
document.write( "* n = Number of Periods (58)\r<BR>\n" );
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document.write( "Rearrange the formula to solve for M:\r<BR>\n" );
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document.write( "M = PV / [((1 - (1 + r)^-n) / r) * (1 + r)]\r<BR>\n" );
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document.write( "M = 32944.08 / [((1 - (1.00775)^-58) / 0.00775) * (1.00775)]<BR>\n" );
document.write( "M = 32944.08 / [((1 - 0.62791485) / 0.00775) * 1.00775]<BR>\n" );
document.write( "M = 32944.08 / [(0.37208515 / 0.00775) * 1.00775]<BR>\n" );
document.write( "M = 32944.08 / [48.010987 * 1.00775]<BR>\n" );
document.write( "M = 32944.08 / 48.382093<BR>\n" );
document.write( "M ≈ $681.09\r<BR>\n" );
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document.write( "**Answer:**\r<BR>\n" );
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document.write( "You will be able to withdraw approximately $681.09 each month.<BR>\n" );
document.write( " </SPAN>\n" );
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