document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172706>Question 1172706</A>: <I><SPAN STYLE=\"word-break: break-all;\"> As part of your retirement plan, you have decided to deposit $6,000 at the beginning of each year into an account paying 5% interest compounded annually. (Round your answers to the nearest cent.)\r<BR>\n" );
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document.write( "How much (in $) would the account be worth after 10 years? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850808 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</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=850808\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Certainly! Let's break down how to calculate the future value of your retirement account.\r<BR>\n" );
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document.write( "**Understanding the Problem**\r<BR>\n" );
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document.write( "This is an example of an annuity due, where payments are made at the beginning of each period.\r<BR>\n" );
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document.write( "**Formula**\r<BR>\n" );
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document.write( "The formula for the future value (FV) of an annuity due is:\r<BR>\n" );
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document.write( "FV = P * [((1 + r)^n - 1) / r] * (1 + r)\r<BR>\n" );
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document.write( "Where:\r<BR>\n" );
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document.write( "* P = periodic payment ($6,000)<BR>\n" );
document.write( "* r = annual interest rate (5% or 0.05)<BR>\n" );
document.write( "* n = number of years (10)\r<BR>\n" );
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document.write( "**Calculation**\r<BR>\n" );
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document.write( "1.  **Plug in the values:**<BR>\n" );
document.write( "    FV = 6000 * [((1 + 0.05)^10 - 1) / 0.05] * (1 + 0.05)\r<BR>\n" );
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document.write( "2.  **Calculate (1 + 0.05)^10:**<BR>\n" );
document.write( "    (1.05)^10 ≈ 1.62889462678\r<BR>\n" );
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document.write( "3.  **Calculate ((1 + 0.05)^10 - 1):**<BR>\n" );
document.write( "    1.62889462678 - 1 ≈ 0.62889462678\r<BR>\n" );
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document.write( "4.  **Divide by 0.05:**<BR>\n" );
document.write( "    0.62889462678 / 0.05 ≈ 12.5778925356\r<BR>\n" );
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document.write( "5.  **Multiply by 6000:**<BR>\n" );
document.write( "    12.5778925356 * 6000 ≈ 75467.3552136\r<BR>\n" );
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document.write( "6.  **Multiply by 1.05:**<BR>\n" );
document.write( "    75467.3552136 * 1.05 ≈ 79240.7229743\r<BR>\n" );
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document.write( "7.  **Round to the nearest cent:**<BR>\n" );
document.write( "    $79,240.72\r<BR>\n" );
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document.write( "**Answer**\r<BR>\n" );
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document.write( "The account would be worth approximately $79,240.72 after 10 years.<BR>\n" );
document.write( " </SPAN>\n" );
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