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 #850318 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52787)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850318\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "What is the present worth of a P250 annuity starting at the end of the third year <BR>\n" );
document.write( "and continuing to the end of the fourth year, if the annual interest rate is 5%? <BR>\n" );
document.write( "With cash flow diagram.<BR>\n" );
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document.write( "I will use slightly different logic comparing with @CPhill.\r<BR>\n" );
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document.write( "The cash flow diagram\r\n" );
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document.write( "Years     1      2      3       4   \r\n" );
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document.write( "Deposits  0      0     250     250\r\n" );
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document.write( "Amount    0      0     250     250 + 0.05*250 + 250 = 512.50.\r\n" );
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document.write( "                       end     end        \r\n" );
document.write( "                       of the  of the\r\n" );
document.write( "                       year    year\r\n" );
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document.write( "In this problem, the amount at the account is P250 at the end of the 3rd year \r\n" );
document.write( "(after first depositing), and it is not a subject of compounding at the end of the year 3.\r\n" );
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document.write( "First compounding will happen at the end of the 4th year, and immediately after that \r\n" );
document.write( "the next amount of P250 will be deposited, giving the total at the end of year 4 as \r\n" );
document.write( "250 + 0.05*250 + 250 = 512.50.\r\n" );
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document.write( "So, at the end of the 4th year, after first compounding and the second deposit, \r\n" );
document.write( "the amount at the account is 512.50.\r\n" );
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document.write( "To get the present value for \"now\", which is the beginning of the year 1, we should rewind \r\n" );
document.write( "this amount of P512.50 4 (four) years back.\r\n" );
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document.write( "So, the present value is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=512.50%2F%281%2B0.05%29%5E4 ALIGN=MIDDLE  ALT=\"512.50%2F%281%2B0.05%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=512.50%2F1.05%5E4 ALIGN=MIDDLE  ALT=\"512.50%2F1.05%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = P421.64  (rounded).\r\n" );
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document.write( "<U>ANSWER</U>.  The present value is  P421.64  (rounded).\r\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "Below is my comment to Edwin's post.\r<BR>\n" );
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document.write( "Edwin, I did not get, to which address did you directed/targeted your post - to mine or <BR>\n" );
document.write( "to the address of @CPhill, who solves here old problems one after another in numbers of hundreds ?\r<BR>\n" );
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document.write( "Edwin, you see students everywhere.  \r<BR>\n" );
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document.write( "Stop, your students are a myth, they are mythical.\r<BR>\n" );
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document.write( "Just starting from the year 2021 we all at this forum work almost exclusively <BR>\n" );
document.write( "for AI (= Artificial Intelligence), without knowing it, without understanding it <BR>\n" );
document.write( "and without even suspecting it.\r<BR>\n" );
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document.write( "In the school, nobody will give such problem to a student, because it is one level above the school level.\r<BR>\n" );
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document.write( "Also, after posting a problem and responding a solution, this solution is viewed by others 15 times<BR>\n" );
document.write( "in the archive, according to the statistic.\r<BR>\n" );
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document.write( "So, your notice is interesting, but irrelevant to the process of functioning of this forum.\r<BR>\n" );
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document.write( "Have a nice day !\r<BR>\n" );
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document.write( " </SPAN>\n" );
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