document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173174>Question 1173174</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A local university is planning to invest $500,000 every 3 months in an investment which earns interest at the rate of 12% per year compounded quarterly. The first investment will be at the end of this current quarter. a) To what sum will be the investment grow at the end of 5 years. b) How much interest will be earned during this period? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850749 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=850749\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break down this investment problem step-by-step:\r<BR>\n" );
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document.write( "**a) To what sum will the investment grow at the end of 5 years?**\r<BR>\n" );
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document.write( "1.  **Identify the variables:**<BR>\n" );
document.write( "    * Payment (PMT): $500,000<BR>\n" );
document.write( "    * Interest rate per year (r): 12% or 0.12<BR>\n" );
document.write( "    * Compounding frequency (n): Quarterly, so 4 times per year<BR>\n" );
document.write( "    * Interest rate per period (i): r/n = 0.12 / 4 = 0.03<BR>\n" );
document.write( "    * Number of years (t): 5<BR>\n" );
document.write( "    * Total number of periods (N): t * n = 5 * 4 = 20\r<BR>\n" );
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document.write( "2.  **Use the future value of an ordinary annuity formula:**\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( "3.  **Plug in the values:**\r<BR>\n" );
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document.write( "    * FV = $500,000 * [((1 + 0.03)^20 - 1) / 0.03]<BR>\n" );
document.write( "    * FV = $500,000 * [((1.03)^20 - 1) / 0.03]<BR>\n" );
document.write( "    * FV = $500,000 * [(1.80611123467 - 1) / 0.03]<BR>\n" );
document.write( "    * FV = $500,000 * [0.80611123467 / 0.03]<BR>\n" );
document.write( "    * FV = $500,000 * 26.870374489<BR>\n" );
document.write( "    * FV = $13,435,187.24 (approximately)\r<BR>\n" );
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document.write( "Therefore, the investment will grow to approximately $13,435,187.24 at the end of 5 years.\r<BR>\n" );
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document.write( "**b) How much interest will be earned during this period?**\r<BR>\n" );
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document.write( "1.  **Calculate the total amount invested:**<BR>\n" );
document.write( "    * Total investment = PMT * N = $500,000 * 20 = $10,000,000\r<BR>\n" );
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document.write( "2.  **Calculate the total interest earned:**<BR>\n" );
document.write( "    * Total interest = FV - Total investment<BR>\n" );
document.write( "    * Total interest = $13,435,187.24 - $10,000,000<BR>\n" );
document.write( "    * Total interest = $3,435,187.24\r<BR>\n" );
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document.write( "Therefore, the total interest earned during this period will be approximately $3,435,187.24.<BR>\n" );
document.write( " </SPAN>\n" );
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