document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173154>Question 1173154</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A person wants to deposit $10,000 per year for 6 years. If interest is earned at the rate of<BR>\n" );
document.write( "10 percent per year, compute the amount to which the deposits will grow by the end of the 6 years if:<BR>\n" );
document.write( "(a) Deposits of $10,000 are made at the end of each year with interest compounded annually.<BR>\n" );
document.write( "(b) Deposits of $5,000 are made at the end of each 6-month period with interest com pounded semiannually.<BR>\n" );
document.write( "(e) Deposits of $2,500 are made at the end of every quarter with interest compounded </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850754 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=850754\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break down each scenario and calculate the future value of the deposits:\r<BR>\n" );
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document.write( "**(a) Annual Deposits of $10,000**\r<BR>\n" );
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document.write( "* **Deposit (PMT):** $10,000<BR>\n" );
document.write( "* **Interest Rate (r):** 10% or 0.10<BR>\n" );
document.write( "* **Number of Years (n):** 6<BR>\n" );
document.write( "* **Compounding:** Annually\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( "FV = $10,000 * [((1 + 0.10)^6 - 1) / 0.10]<BR>\n" );
document.write( "FV = $10,000 * [(1.10^6 - 1) / 0.10]<BR>\n" );
document.write( "FV = $10,000 * [(1.771561 - 1) / 0.10]<BR>\n" );
document.write( "FV = $10,000 * [0.771561 / 0.10]<BR>\n" );
document.write( "FV = $10,000 * 7.71561<BR>\n" );
document.write( "FV = $77,156.10\r<BR>\n" );
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document.write( "**(b) Semi-annual Deposits of $5,000**\r<BR>\n" );
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document.write( "* **Deposit (PMT):** $5,000<BR>\n" );
document.write( "* **Annual Interest Rate (r):** 10% or 0.10<BR>\n" );
document.write( "* **Semi-annual Interest Rate (i):** 0.10 / 2 = 0.05<BR>\n" );
document.write( "* **Number of Years (n):** 6<BR>\n" );
document.write( "* **Number of Periods (N):** 6 * 2 = 12<BR>\n" );
document.write( "* **Compounding:** Semi-annually\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( "FV = $5,000 * [((1 + 0.05)^12 - 1) / 0.05]<BR>\n" );
document.write( "FV = $5,000 * [(1.05^12 - 1) / 0.05]<BR>\n" );
document.write( "FV = $5,000 * [(1.795856 - 1) / 0.05]<BR>\n" );
document.write( "FV = $5,000 * [0.795856 / 0.05]<BR>\n" );
document.write( "FV = $5,000 * 15.917127<BR>\n" );
document.write( "FV = $79,585.64\r<BR>\n" );
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document.write( "**(c) Quarterly Deposits of $2,500**\r<BR>\n" );
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document.write( "* **Deposit (PMT):** $2,500<BR>\n" );
document.write( "* **Annual Interest Rate (r):** 10% or 0.10<BR>\n" );
document.write( "* **Quarterly Interest Rate (i):** 0.10 / 4 = 0.025<BR>\n" );
document.write( "* **Number of Years (n):** 6<BR>\n" );
document.write( "* **Number of Periods (N):** 6 * 4 = 24<BR>\n" );
document.write( "* **Compounding:** Quarterly\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( "FV = $2,500 * [((1 + 0.025)^24 - 1) / 0.025]<BR>\n" );
document.write( "FV = $2,500 * [(1.025^24 - 1) / 0.025]<BR>\n" );
document.write( "FV = $2,500 * [(1.808734 - 1) / 0.025]<BR>\n" );
document.write( "FV = $2,500 * [0.808734 / 0.025]<BR>\n" );
document.write( "FV = $2,500 * 32.34936<BR>\n" );
document.write( "FV = $80,873.40\r<BR>\n" );
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document.write( "**Summary**\r<BR>\n" );
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document.write( "* **(a)** $77,156.10<BR>\n" );
document.write( "* **(b)** $79,585.64<BR>\n" );
document.write( "* **(c)** $80,873.40<BR>\n" );
document.write( " </SPAN>\n" );
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