document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1161373>Question 1161373</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) An account starts with a value of $5,900. It earns 6.3%, compounded monthly. $200 is added to the account at the end of each month. What will the account balance be after 41 years?\r<BR>\n" );
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document.write( "Note: It is important that you do TWO calculations and round each one to the nearest penny to avoid a possible one-penny rounding issue.\r<BR>\n" );
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document.write( "Answer = $\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #785050 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=785050\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you've got two investments.<BR>\n" );
document.write( "the first is 59,000 invested up front at 6.3% per year compounded monthly.<BR>\n" );
document.write( "the second is 200 invested at the end of each month at 6.3% per year compounded monthly.<BR>\n" );
document.write( "you can put this in a financial calculator and the calculator will do the computations for you.<BR>\n" );
document.write( "your inputs would be:<BR>\n" );
document.write( "present value = -59000 (negative because it's money going out from you)<BR>\n" );
document.write( "future value = what you want to find<BR>\n" );
document.write( "payments at the end of each month are -200 (negative because it's money going out from you.<BR>\n" );
document.write( "interest rate is 6.3/12 = .525% per month.<BR>\n" );
document.write( "the 59000 is invested at the beginning of the investment period.<BR>\n" );
document.write( "the 200 is invested at the end of each month.<BR>\n" );
document.write( "calculator says that the future value is 1,238,479.26<BR>\n" );
document.write( "if you do the calculations separately, then the first calculation (the 59000 invested up front) will have a future value of 775,7111.5267.<BR>\n" );
document.write( "the second calculation (the 200 at the end of each month) will have a future value of 462,767.7332.<BR>\n" );
document.write( "add these together (without rounding to the nearest penny) and you get a combined future value of 1,238,479.2599 rounded to 4 decimal places which becomes 1,238,479.26 rounded to 2 decimal places.<BR>\n" );
document.write( "if you rounded each separate calculation to the nearest penny, then the combined total would be 1,238,479.26.<BR>\n" );
document.write( "there is no discrepancy because the first figure is rounded up and the second figure is rounded down.<BR>\n" );
document.write( "algebraically, you should not found until the very end, which is when the final figures are added together.<BR>\n" );
document.write( "financially, it's probably up to the policies of the financial institution whether they round after combining the figures or round after combining the figures.<BR>\n" );
document.write( "if the investments are in the same account then i would assume the rounding is done once at the end after the figures are tallied together.<BR>\n" );
document.write( "however, i don't know what the individual financial institution policies are, so i can't say definitively, one way or the other.<BR>\n" );
document.write( "i used a financial calculator.<BR>\n" );
document.write( "you could also use formulas and calculate from them.<BR>\n" );
document.write( "future value of 59000 at 6.3% compounded annually would give you the following equation:<BR>\n" );
document.write( "f = 59000 * (1 + .063/12) ^ (41 * 12) = 775,711.5267<BR>\n" );
document.write( "future value of 200 at the end of each month at 6.3% cmpounded annually would give you the following equation:<BR>\n" );
document.write( "f = (200 * ((1 + .063/12) ^ (41*12) -1)) / (.063/12) = 462,767.7332<BR>\n" );
document.write( "these are the same values i got using the financial calculator, as they should be.<BR>\n" );
document.write( "here are the results from using the online financial calculator at <a  rel=nofollow HREF= \"https://arachnoid.com/finance/index.html\" target = \"_blank\">https://arachnoid.com/finance/index.html</a><BR>\n" );
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document.write( "the investments are shown as negative because it's money going out.<BR>\n" );
document.write( "the future value is shown as positive because it's money coming in.<BR>\n" );
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