document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1143508>Question 1143508</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A businessman borrowed P3,000,000 with interest at the rate of 6% compounded annually. He agrees to discharge his obligations by paying  series of 6 annual payment,the first being due at the end of the fifth year. Determine the value of his annual payment.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #764465 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=764465\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> he will make 6 payments at the end of each year starting from the end of the firth year.\r<BR>\n" );
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document.write( "the interest rate is 6% per year.\r<BR>\n" );
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document.write( "the present value of the loan is 3,000,000 at the end of year 0.\r<BR>\n" );
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document.write( "the end of year 0 is the same time point as the beginning of year 1.\r<BR>\n" );
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document.write( "the future value of this loan at the end of year 4 is equal to 3,000,000 * 1.06^4 = 3,787,430.88.\r<BR>\n" );
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document.write( "3,787,430.88 is the present value of the loan at the end of year 4.\r<BR>\n" );
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document.write( "the end of year 4 is the same time point as the beginning of year 5.\r<BR>\n" );
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document.write( "there are 6 annual payments starting at the end of year 5.\r<BR>\n" );
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document.write( "what you have, therefore, is the following inputs to a financial calculator.\r<BR>\n" );
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document.write( "present value = 3,787,430.88.<BR>\n" );
document.write( "future value = 0<BR>\n" );
document.write( "number of time periods = 6<BR>\n" );
document.write( "interest rate per time period = 6%<BR>\n" );
document.write( "payments are made at the end of each time period.\r<BR>\n" );
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document.write( "the calculator then tells you that the payments at the end of year year need to be 770,221.90.\r<BR>\n" );
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document.write( "that is your solution.\r<BR>\n" );
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document.write( "the calculator i used can be found at <a  rel=nofollow HREF= \"https://arachnoid.com/finance/\" target = \"_blank\">https://arachnoid.com/finance/</a>\r<BR>\n" );
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document.write( "here's a display of the results using this calculator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/073101.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "i also did a cash flow analysis using excel.\r<BR>\n" );
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document.write( "here's a display of the results of that cash flow analysis.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/073102.jpg\" alt=\"$$$\">\r<BR>\n" );
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document.write( "boy means beginning of year.<BR>\n" );
document.write( "eoy means end of year.\r<BR>\n" );
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document.write( "these are the time points.\r<BR>\n" );
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document.write( "the beginning of year 1 is the same time point as the end of year 0.<BR>\n" );
document.write( "the beginning of year 5 is the same time point as the end of year 4.\r<BR>\n" );
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document.write( "column F is the loan<BR>\n" );
document.write( "column G is the payments on that loan.<BR>\n" );
document.write( "column H is the remaining balance of the loan.\r<BR>\n" );
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document.write( "the calculations for the remaining balance of the loan are:\r<BR>\n" );
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document.write( "the remaining balance of the loan at the end of year 0 is the loan itself.\r<BR>\n" );
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document.write( "the remaining balance of the loan at the end of yer 1 is the value of the loan at the end of year 0 * 1.06 minus any payment at the end of year 1.\r<BR>\n" );
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document.write( "this continues for each year.\r<BR>\n" );
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document.write( "at the end of year 5, the remaining balance of the loan is equal to value of the loan at the end of year 4 * 1.06 minus the value of the payment at the end of year 5.\r<BR>\n" );
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document.write( "this becomes $3,787,430.88 * 1.06 = $4,014,676.733 - $770,221.90 = $3,244,454.833, shown as $3,244,454.83.\r<BR>\n" );
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document.write( "this same procedure continues to the end of the loan period where the remaining balance is $.01.\r<BR>\n" );
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document.write( "it is actually $0.00 but there is a small error due to rounding of the payment amount.\r<BR>\n" );
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document.write( "the actual values, without rounding are:\r<BR>\n" );
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document.write( " </SPAN>\n" );
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