document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178747>Question 1178747</A>: <I><SPAN STYLE=\"word-break: break-all;\"> financial planning joe plans to deposit $200 at the end of each month into a bank account for a period of 2 years after which he plans to deposit $300 at the end of each month into the same account for another 3 years if the bank pays interest at the rate of 6% per year compounded monthly how much will joe have in his account by the end of 5 years <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850302 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=850302\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break this problem into two parts to find the total amount Joe will have in his account.\r<BR>\n" );
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document.write( "**Part 1: First 2 Years of $200 Deposits**\r<BR>\n" );
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document.write( "1.  **Monthly Deposit:** $200<BR>\n" );
document.write( "2.  **Time Period:** 2 years<BR>\n" );
document.write( "3.  **Interest Rate:** 6% per year compounded monthly (0.06 / 12 = 0.005 per month)<BR>\n" );
document.write( "4.  **Number of Deposits:** 2 years * 12 months/year = 24 deposits\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 = PMT * [((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( "* PMT = Periodic Payment ($200)<BR>\n" );
document.write( "* r = Interest Rate per Period (0.005)<BR>\n" );
document.write( "* n = Number of Periods (24)\r<BR>\n" );
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document.write( "FV₁ = 200 * [((1 + 0.005)^24 - 1) / 0.005]<BR>\n" );
document.write( "FV₁ = 200 * [(1.005^24 - 1) / 0.005]<BR>\n" );
document.write( "FV₁ = 200 * [(1.127159776 - 1) / 0.005]<BR>\n" );
document.write( "FV₁ = 200 * [0.127159776 / 0.005]<BR>\n" );
document.write( "FV₁ = 200 * 25.4319552<BR>\n" );
document.write( "FV₁ ≈ $5086.39\r<BR>\n" );
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document.write( "**Part 2: Next 3 Years of $300 Deposits**\r<BR>\n" );
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document.write( "1.  **Monthly Deposit:** $300<BR>\n" );
document.write( "2.  **Time Period:** 3 years<BR>\n" );
document.write( "3.  **Interest Rate:** 6% per year compounded monthly (0.06 / 12 = 0.005 per month)<BR>\n" );
document.write( "4.  **Number of Deposits:** 3 years * 12 months/year = 36 deposits\r<BR>\n" );
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document.write( "We'll use the future value of an ordinary annuity formula again, but we also need to account for the FV₁ amount that has been accruing interest for the entire 5 years.\r<BR>\n" );
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document.write( "First calculate the future value of the first 2 years after 5 years.\r<BR>\n" );
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document.write( "FV1_5 = FV1 * (1.005)^36<BR>\n" );
document.write( "FV1_5 = 5086.39 * (1.005)^36<BR>\n" );
document.write( "FV1_5 = 5086.39 * 1.196680526<BR>\n" );
document.write( "FV1_5 = $6086.07\r<BR>\n" );
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document.write( "Then calculate the future value of the next 3 years.\r<BR>\n" );
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document.write( "FV₂ = 300 * [((1 + 0.005)^36 - 1) / 0.005]<BR>\n" );
document.write( "FV₂ = 300 * [(1.005^36 - 1) / 0.005]<BR>\n" );
document.write( "FV₂ = 300 * [(1.196680526 - 1) / 0.005]<BR>\n" );
document.write( "FV₂ = 300 * [0.196680526 / 0.005]<BR>\n" );
document.write( "FV₂ = 300 * 39.3361052<BR>\n" );
document.write( "FV₂ ≈ $11800.83\r<BR>\n" );
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document.write( "**Total Amount in Account:**\r<BR>\n" );
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document.write( "* Total = FV1_5 + FV₂<BR>\n" );
document.write( "* Total = $6086.07 + $11800.83<BR>\n" );
document.write( "* Total = $17886.90\r<BR>\n" );
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document.write( "**Answer:**\r<BR>\n" );
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document.write( "Joe will have approximately $17,886.90 in his account by the end of 5 years.<BR>\n" );
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