document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191376>Question 1191376</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How much would you need to deposit in an account each month in order to have $50,000 in the account in 7 years? Assume the account earns 6% interest. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849166 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=849166\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to figure out the monthly deposit you'd need:\r<BR>\n" );
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document.write( "**1. Understand the Problem**\r<BR>\n" );
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document.write( "This is a future value of an ordinary annuity problem. We need to find the regular payment (monthly deposit) that will result in a specific future value ($50,000) given an interest rate (6%) and a time period (7 years).\r<BR>\n" );
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document.write( "**2. Use the Formula**\r<BR>\n" );
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document.write( "The future value of an ordinary annuity formula is:\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 ($50,000)<BR>\n" );
document.write( "* P = Periodic Payment (what we want to find)<BR>\n" );
document.write( "* r = Interest rate per period (6% annual rate / 12 months = 0.06/12 = 0.005)<BR>\n" );
document.write( "* n = Number of periods (7 years * 12 months = 84)\r<BR>\n" );
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document.write( "**3. Solve for P**\r<BR>\n" );
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document.write( "We need to rearrange the formula to solve for the periodic payment (P):\r<BR>\n" );
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document.write( "P = FV * [r / ((1 + r)^n - 1)]\r<BR>\n" );
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document.write( "**4. Plug in the Values and Calculate**\r<BR>\n" );
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document.write( "P = $50,000 * [0.005 / ((1 + 0.005)^84 - 1)]<BR>\n" );
document.write( "P = $50,000 * [0.005 / (1.517 - 1)]<BR>\n" );
document.write( "P = $50,000 * [0.005 / 0.517]<BR>\n" );
document.write( "P ≈ $483.37\r<BR>\n" );
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document.write( "**Answer:** You would need to deposit approximately $483.37 each month to have $50,000 in the account after 7 years.<BR>\n" );
document.write( " </SPAN>\n" );
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