document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1076571>Question 1076571</A>: <I><SPAN STYLE=\"word-break: break-all;\"> . How much do you have to deposit today so that beginning 11 years from now you can withdraw 10,000 euros a year for the next five years (periods 11 through 15) plus an additional amount of 20,000 euros in the last year (period 15)? Assume an interest rate of 6% compounded annually. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #691234 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=691234\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the easiest way to solve this is find the net present value of your cash flows.\r<BR>\n" );
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document.write( "the first thing you want to do is get the present value of the cash flows coming in.\r<BR>\n" );
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document.write( "in order to do that, you need to make sure you have the time points correct.\r<BR>\n" );
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document.write( "time point 0 is the start of the first year<BR>\n" );
document.write( "time point 1 is the end of the first year and the start of the second year.\r<BR>\n" );
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document.write( "you want your first payment to start at the end of the eleventh year.\r<BR>\n" );
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document.write( "that would be time point 11.\r<BR>\n" );
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document.write( "you will be taking out 10,000 in time point 11, 12, 13, 14.\r<BR>\n" );
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document.write( "you will be taking out 30,000 in time point 15.\r<BR>\n" );
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document.write( "you don't know what you will be investing in time point 0 until you get the present value of the cash flows from time point 10 to time point 15.\r<BR>\n" );
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document.write( "once you get that, you will see that the present value of those cash flows is 31, 866.92\r<BR>\n" );
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document.write( "that's how much you need to invest in time point 0 so that you can take your money out starting in time point 11.\r<BR>\n" );
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document.write( "therefore, your cash flow will be -31,866.92 in time point 0, 10,000 in time point 11, 12, 13, 14, and 30,000 in time point 15.\r<BR>\n" );
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document.write( "at the end of time point 15, you should have no money left.\r<BR>\n" );
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document.write( "that's exactly what happens as shown in the following excel printout.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/041404.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "you could also have used a financial calculator to get the same result.\r<BR>\n" );
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document.write( "the details cash flow and the use of the financial calculators should get you the same result or you did something wrong.\r<BR>\n" );
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document.write( "the first thing to do is to find out the present value of 10,000 at the end of each year for 5 years.\r<BR>\n" );
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document.write( "the result of that is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/041405.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the present value is 42,123.64\r<BR>\n" );
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document.write( "that's what you have to invest at the start of the 11th year so you can take out 10,000 for 5 years starting at the end of the 11th year.\r<BR>\n" );
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document.write( "since that is in the start of the 11th year, that is in time point 10.\r<BR>\n" );
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document.write( "you need to get the present value of that at the start of the first year, which is time point 0.\r<BR>\n" );
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document.write( "the result of that calculation is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/041406.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the present value is 23,521.62.\r<BR>\n" );
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document.write( "next you want to take out an additional 20,000 at the end of the 15th year.\r<BR>\n" );
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document.write( "you want to get the present value of that.\r<BR>\n" );
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document.write( "the result of that calculation is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/041407.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the present value is 8,345.30.\r<BR>\n" );
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document.write( "the amount of money that you need to invest in time period 0 is 23,521.62 plus 8,345.30 for a total of 31,866.92\r<BR>\n" );
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document.write( "the detailed present value of net cash flow calculations confirms this solution is correct.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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