document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191374>Question 1191374</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you want to have $800,000 for retirement in 30 years. Your account earns 10% interest<BR>\n" );
document.write( "a) How much would you need to deposit in the account each month?<BR>\n" );
document.write( "b) How much interest will you earn? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849163 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=849163\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate the monthly deposit and the total interest earned:\r<BR>\n" );
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document.write( "**a) Calculating the Monthly Deposit:**\r<BR>\n" );
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document.write( "We'll use the future value of an ordinary annuity formula, which 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 ($800,000)<BR>\n" );
document.write( "* P = Periodic Payment (what we want to find)<BR>\n" );
document.write( "* r = Interest rate per period (10% per year, so 10%/12 per month, or 0.1/12)<BR>\n" );
document.write( "* n = Number of periods (30 years * 12 months/year = 360 months)\r<BR>\n" );
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document.write( "Let's rearrange the formula to solve for 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( "Now, plug in the values:\r<BR>\n" );
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document.write( "P = $800,000 * [(0.1/12) / ((1 + 0.1/12)^360 - 1)]<BR>\n" );
document.write( "P = $800,000 * [0.008333 / (1.008333^360 - 1)]<BR>\n" );
document.write( "P = $800,000 * [0.008333 / (19.788 - 1)]<BR>\n" );
document.write( "P = $800,000 * [0.008333 / 18.788]<BR>\n" );
document.write( "P ≈ $353.91\r<BR>\n" );
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document.write( "So, you would need to deposit approximately $353.91 each month.\r<BR>\n" );
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document.write( "**b) Calculating the Total Interest Earned:**\r<BR>\n" );
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document.write( "1. **Calculate the total amount deposited:**<BR>\n" );
document.write( "   Total Deposited = Monthly Deposit * Number of Months<BR>\n" );
document.write( "   Total Deposited = $353.91 * 360<BR>\n" );
document.write( "   Total Deposited ≈ $127,407.60\r<BR>\n" );
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document.write( "2. **Calculate the total interest earned:**<BR>\n" );
document.write( "   Total Interest Earned = Future Value - Total Deposited<BR>\n" );
document.write( "   Total Interest Earned = $800,000 - $127,407.60<BR>\n" );
document.write( "   Total Interest Earned ≈ $672,592.40\r<BR>\n" );
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document.write( "Therefore, you will earn approximately $672,592.40 in interest.<BR>\n" );
document.write( " </SPAN>\n" );
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