document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177628>Question 1177628</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If an individual determines that they would like to retire in 20 years with $500,000 as the future value that is in their IRA, which earns 6% compounded monthly, how much money (rounded to the nearest cent) should they be putting away into the account each month?\r<BR>\n" );
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document.write( "I need to see the calculations & answers please!\r<BR>\n" );
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document.write( "Homework question from Hans Beauvoir </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850432 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=850432\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To determine the monthly deposit needed to reach $500,000 in 20 years, we can utilize the future value of an ordinary annuity formula.\r<BR>\n" );
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document.write( "The future value of an ordinary annuity is given by:\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "FV = PMT * (((1 + r)^n - 1) / r)<BR>\n" );
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document.write( "Where:\r<BR>\n" );
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document.write( "* FV is the future value ($500,000)<BR>\n" );
document.write( "* PMT is the monthly payment (what we want to find)<BR>\n" );
document.write( "* r is the periodic interest rate (6% per year compounded monthly, so r = 0.06/12 = 0.005)<BR>\n" );
document.write( "* n is the number of periods (20 years with monthly compounding, so n = 20 * 12 = 240)\r<BR>\n" );
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document.write( "Plugging in the values:\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "$500,000 = PMT * (((1 + 0.005)^240 - 1) / 0.005)<BR>\n" );
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document.write( "Solving for PMT:\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "PMT = $500,000 / (((1 + 0.005)^240 - 1) / 0.005)<BR>\n" );
document.write( "```\r<BR>\n" );
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document.write( "PMT ≈ $1,285.17<BR>\n" );
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document.write( "Therefore, the individual should deposit approximately **$1,285.17** each month to reach their retirement goal.\r<BR>\n" );
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document.write( "Let me know if you would like to explore other scenarios, such as different interest rates or time horizons. </SPAN>\n" );
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