document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164349>Question 1164349</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given $400,000 today, determine the equivalent series of 24 semi annual payments which could be generated beginning in 6 months. Assume interest can be earned at a rate of 7 percent per year compounded semi annually.\r<BR>\n" );
document.write( "\n" );
document.write( "where  A= Present value of annuity 400,000\r<BR>\n" );
document.write( "\n" );
document.write( "i= interest rate per period = 0.07/2 = 0.035\r<BR>\n" );
document.write( "\n" );
document.write( "n = number of annuity </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #788778 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=788778\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a financial calculator makes this pretty easy.<BR>\n" );
document.write( "it is an annuity with payments at the end of each time period, with each time period being equal to half a year, with a  half a year being equivalent to 6 months.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "using the financial calculator, you would provide the folloiwng information.<BR>\n" );
document.write( "present value = -400,000.<BR>\n" );
document.write( "future value = 0<BR>\n" );
document.write( "interest rate = 7% per year / 2 = 3.5% per semi-annual period.<BR>\n" );
document.write( "payments are made at the end of each semi-annual period.<BR>\n" );
document.write( "number of semi-annual time periods is 24.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you would provide these inputs and then have the calculator tell you what the semi-annual payments need to be.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "those semi-annual payments need to be equal to 24,909.13.<BR>\n" );
document.write( "since they are made at the end of each semi-annual period, then the first payment is at the end of the first semi-annual period which is 6 months from the time of the investment.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is what the calculator displays after the inputs are made and the PMT button is pressed.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/090601.jpg\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "there is a formula that you can do this manually with using your calculator.<BR>\n" );
document.write( "that formula is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "ANNUITY FOR A PRESENT AMOUNT WITH END OF TIME PERIOD PAYMENTS\r<BR>\n" );
document.write( "\n" );
document.write( "a = (p*r)/(1-(1/(1+r)^n))\r<BR>\n" );
document.write( "\n" );
document.write( "a is the annuity.<BR>\n" );
document.write( "p is the present amount.<BR>\n" );
document.write( "r is the interest rate per time period.<BR>\n" );
document.write( "n is the number of time periods.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "using that formula, you would do the following:<BR>\n" );
document.write( "p = 400000<BR>\n" );
document.write( "r = .035<BR>\n" );
document.write( "n = 24\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula becomes a = (400000*.035)/(1-(1/(1+.035)^24))<BR>\n" );
document.write( "execute the formula on your calculator to get:<BR>\n" );
document.write( "p = 24909.1321<BR>\n" );
document.write( "round to 2 decimal digits and the answer is the same as given by the calculator.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i used exel to verify this is correct.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the excel printout is shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/090602.jpg\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );