document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172845>Question 1172845</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ron Sample is the grand prize winner in a college tuition essay contest awarded through a local organization's scholarship fund. The winner receives $3,000 at the beginning of each year for the next 5 years. How much (in $) should be invested at 8% interest compounded annually to award the prize? (Round your answer to the nearest cent.)\r<BR>\n" );
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document.write( "I did 3000 x 1-(1+.08)-5/.08 and got $11978.13<BR>\n" );
document.write( "the answer seems pretty high.. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850800 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=850800\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break down this problem. We need to find the present value of an annuity, where Ron Sample receives $3,000 at the beginning of each year for 5 years, and the interest rate is 8% compounded annually.\r<BR>\n" );
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document.write( "Since the payments are made at the beginning of each year, this is an annuity due.\r<BR>\n" );
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document.write( "**Formula for Present Value of an Annuity Due:**\r<BR>\n" );
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document.write( "PV = PMT * [(1 - (1 + r)^-n) / r] * (1 + r)\r<BR>\n" );
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document.write( "Where:\r<BR>\n" );
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document.write( "* PV = Present Value<BR>\n" );
document.write( "* PMT = Payment per period ($3,000)<BR>\n" );
document.write( "* r = Interest rate per period (8% or 0.08)<BR>\n" );
document.write( "* n = Number of periods (5 years)\r<BR>\n" );
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document.write( "**Calculation:**\r<BR>\n" );
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document.write( "PV = 3000 * [(1 - (1 + 0.08)^-5) / 0.08] * (1 + 0.08)\r<BR>\n" );
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document.write( "1.  Calculate (1 + 0.08)^-5:<BR>\n" );
document.write( "    * (1.08)^-5 ≈ 0.6805832\r<BR>\n" );
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document.write( "2.  Calculate 1 - (1 + 0.08)^-5:<BR>\n" );
document.write( "    * 1 - 0.6805832 ≈ 0.3194168\r<BR>\n" );
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document.write( "3.  Divide by 0.08:<BR>\n" );
document.write( "    * 0.3194168 / 0.08 ≈ 3.99271\r<BR>\n" );
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document.write( "4.  Multiply by 1.08:<BR>\n" );
document.write( "    * 3.99271 * 1.08 ≈ 4.3121268\r<BR>\n" );
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document.write( "5.  Multiply by 3000:<BR>\n" );
document.write( "    * 4.3121268 * 3000 ≈ 12936.3804\r<BR>\n" );
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document.write( "6. Round to the nearest cent.<BR>\n" );
document.write( "    * 12936.38\r<BR>\n" );
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document.write( "Therefore, approximately $12,936.38 should be invested at 8% interest compounded annually to award the prize.<BR>\n" );
document.write( " </SPAN>\n" );
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