document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178719>Question 1178719</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the present worth of a P250 annuity starting at the end of the third year and continuing to the end of the fourth year, if the annual interest rate is 5%? With cash flow diagram. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850303 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=850303\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break down this problem to find the present worth of the annuity.\r<BR>\n" );
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document.write( "**Understanding the Annuity:**\r<BR>\n" );
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document.write( "* **Annuity Amount (PMT):** P250<BR>\n" );
document.write( "* **Start Time:** End of the third year<BR>\n" );
document.write( "* **End Time:** End of the fourth year<BR>\n" );
document.write( "* **Annual Interest Rate (r):** 5% or 0.05\r<BR>\n" );
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document.write( "**Cash Flow Diagram:**\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "Time (Years):   0       1       2       3       4<BR>\n" );
document.write( "Cash Flow:      0       0       0       250     250<BR>\n" );
document.write( "```\r<BR>\n" );
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document.write( "**Calculations:**\r<BR>\n" );
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document.write( "1.  **Present Value at the End of Year 2:**\r<BR>\n" );
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document.write( "    * We need to calculate the present value of the annuity payments at the end of the second year (one year before the first payment).<BR>\n" );
document.write( "    * This is a simple two-payment annuity.<BR>\n" );
document.write( "    * Use the present value of an ordinary annuity formula:<BR>\n" );
document.write( "        * PV = PMT * [(1 - (1 + r)^-n) / r]<BR>\n" );
document.write( "        * PV = 250 * [(1 - (1.05)^-2) / 0.05]<BR>\n" );
document.write( "        * PV = 250 * [(1 - 0.907029478) / 0.05]<BR>\n" );
document.write( "        * PV = 250 * [0.092970522 / 0.05]<BR>\n" );
document.write( "        * PV = 250 * 1.85941044<BR>\n" );
document.write( "        * PV ≈ 464.85261<BR>\n" );
document.write( "    * This means that at the end of year 2, the payments are worth about P464.85\r<BR>\n" );
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document.write( "2.  **Present Value at Time 0 (Now):**\r<BR>\n" );
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document.write( "    * Now, we need to discount the present value at the end of year 2 back to the present (time 0).<BR>\n" );
document.write( "    * PV(at t=0) = PV(at t=2) / (1 + r)^2<BR>\n" );
document.write( "    * PV(at t=0) = 464.85261 / (1.05)^2<BR>\n" );
document.write( "    * PV(at t=0) = 464.85261 / 1.1025<BR>\n" );
document.write( "    * PV(at t=0) ≈ 421.63502\r<BR>\n" );
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document.write( "**Therefore, the present worth of the P250 annuity is approximately P421.64.**<BR>\n" );
document.write( " </SPAN>\n" );
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