document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131198>Question 1131198</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me find this answer for this question\r<BR>\n" );
document.write( "\n" );
document.write( "How much should you invest each month in order to have $500,000 if your rate of return is 6.4% compounded monthly and you want to achieve your goal in 40 years?\r<BR>\n" );
document.write( "\n" );
document.write( "$\r<BR>\n" );
document.write( "\n" );
document.write( "How much interest will you earn?\r<BR>\n" );
document.write( "\n" );
document.write( "$\r<BR>\n" );
document.write( "\n" );
document.write( "How much should you invest each month in order to have $500,000 if you want to achieve your goal in 20 years?\r<BR>\n" );
document.write( "\n" );
document.write( "$\r<BR>\n" );
document.write( "\n" );
document.write( "If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?\r<BR>\n" );
document.write( "\n" );
document.write( "$ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #747899 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=747899\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How much should you invest at the end of each month in order to have $500,000 if your rate of return is 6.4% compounded monthly and you want to achieve your goal in 40 years? \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "How much interest will you earn? \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "$225.07\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "How much should you invest each month in order to have $500,000 if you want to achieve your goal in 20 years? \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "$1031.82\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years? \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "$946,628.83\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the use of a financial calculator helps to get the answers to these questions.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the one i used online can be found at <a  rel=nofollow HREF= \"https://arachnoid.com/finance/\" target = \"_blank\">https://arachnoid.com/finance/</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for your first problem, the inputs are::\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "present value = 0<BR>\n" );
document.write( "future value = 500,000<BR>\n" );
document.write( "number of time periods = 40 * 12 = 480<BR>\n" );
document.write( "interest rate per time period = 6.4 / 12 = .5333333.....<BR>\n" );
document.write( "payment are to be made at the end of each time period.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you then click on pmt and the calculator tells you that the monthly payments need to be $225.07.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "they are shown as minus because it's money going out from you.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's the display.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/120901.jpg\" alt=\"$$$\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for your second problem, the inputs are the same except for number of time periods, which are 20 * 12 = 240.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you then click on pmt and the calculator tells you that the monthly payments are $1031.82.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "they are shown as minus because it's money going out from you.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's the display.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/120902.jpg\" alt=\"$$$\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for your third period, the inputs are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "present value = -500,000<BR>\n" );
document.write( "number of time periods = 10 * 12 = 120<BR>\n" );
document.write( "interest rate per time period = 6.4 / 12 = .5333333.....<BR>\n" );
document.write( "payments per time period = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you then click on fv and the calculator tells you that the future value in 10 years is $946,628.83\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the present value is entered as minus because it's money going out from you.<BR>\n" );
document.write( "the future value is shown as positive because it's money coming back to you.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/120903.jpg\" alt=\"$$$\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "using my TI-BA-II financnail calculator, i got slightly different results, the difference having to do with rounding in the online calculator.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "my TI-BA-II gave me the following results.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for the first problem, monthly payment = 225.0708662 which can be rounded to 225.07.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for the second problem, monthly payment = 1031.821058 which can be rounded to 1031.82.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for the third problem, future value = 946,629.2109 which can be rounded to 946,629.21.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the monthly payments between the online calculator and the TI-BA-II are the same after rounding.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the future value is not.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the reason has to do with internal rounding in the online calculator.<BR>\n" );
document.write( "it truncates, or rounds, the interest rate to .533333.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that leads to a different future value because 6.4/12 is really .53333333........\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the reason i tell you this is just to clue you in to the fact that you could get different answers depending on the calculator that you use.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "which one is more accurate?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in this case, the TI-BA-II gives you the more accurate result.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );