document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209929>Question 1209929</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Pireras are planning to go to Europe 4 years from now and have agreed to set aside $180/month for their trip. If they deposit this money at the en each month into a savings account paying interest at the rate of 3%/year compounded monthly, how much money will be in their ‘travel fund at the end of the fourth year? (Round your answer to the nearest cent.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851070 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=851070\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break down this problem step by step.\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.<BR>\n" );
document.write( "* The Pireras deposit $180 at the end of each month.<BR>\n" );
document.write( "* The interest rate is 3% per year, compounded monthly.<BR>\n" );
document.write( "* The time period is 4 years.\r<BR>\n" );
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document.write( "**2. Identify the Variables**\r<BR>\n" );
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document.write( "* Monthly payment (PMT) = $180<BR>\n" );
document.write( "* Annual interest rate (r) = 3% = 0.03<BR>\n" );
document.write( "* Monthly interest rate (i) = r / 12 = 0.03 / 12 = 0.0025<BR>\n" );
document.write( "* Number of years (t) = 4<BR>\n" );
document.write( "* Number of payments (n) = t * 12 = 4 * 12 = 48\r<BR>\n" );
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document.write( "**3. Apply the Future Value of an Ordinary Annuity Formula**\r<BR>\n" );
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document.write( "The formula is:\r<BR>\n" );
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document.write( "FV = PMT * [((1 + i)^n - 1) / i]\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 = Monthly Payment<BR>\n" );
document.write( "* i = Monthly Interest Rate<BR>\n" );
document.write( "* n = Number of Payments\r<BR>\n" );
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document.write( "**4. Calculate the Future Value**\r<BR>\n" );
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document.write( "FV = 180 * [((1 + 0.0025)^48 - 1) / 0.0025]<BR>\n" );
document.write( "FV = 180 * [((1.0025)^48 - 1) / 0.0025]\r<BR>\n" );
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document.write( "Let's calculate (1.0025)^48 first:\r<BR>\n" );
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document.write( "(1.0025)^48 ≈ 1.1273383\r<BR>\n" );
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document.write( "Now, plug that into the formula:\r<BR>\n" );
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document.write( "FV = 180 * [(1.1273383 - 1) / 0.0025]<BR>\n" );
document.write( "FV = 180 * [0.1273383 / 0.0025]<BR>\n" );
document.write( "FV = 180 * 50.93532<BR>\n" );
document.write( "FV ≈ 9168.3576\r<BR>\n" );
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document.write( "**5. Round to the Nearest Cent**\r<BR>\n" );
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document.write( "FV ≈ $9168.36\r<BR>\n" );
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document.write( "**Answer:** The Pireras will have approximately $9168.36 in their travel fund at the end of the fourth year.<BR>\n" );
document.write( " </SPAN>\n" );
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