document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193988>Question 1193988</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the present value and amount of a sequence of monthly payments of P7,500 with the first payment due at the end of 1 year and the last payment at the end of 5 years. Assume money is worth 10.5% compounded monthly. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #826304 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=826304\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sequence of monthly payments with the first payment due at the end of 1 year and the last payment due at the end of 5 years.<BR>\n" );
document.write( "money is worth 10.5% per year compounded monthly.<BR>\n" );
document.write( "monthly payments are 7500.<BR>\n" );
document.write( "the monthly payments will be for 48 months from the end of month 12 to the end of month 59.<BR>\n" );
document.write( "the monthly interest rate will be 10.5/12 = .875%.<BR>\n" );
document.write( "the present value of the payments will be equal to 292,930.08.<BR>\n" );
document.write( "this present value will be at the end of the 11th month, since the first payment was at the end of the 12th month.<BR>\n" );
document.write( "it needs to be brought back to the the beginning of the first month which is the end of month 0.<BR>\n" );
document.write( "the present value will be 292,930.08 divided by 1.0875 ^ 11 = 266,161.32.<BR>\n" );
document.write( "i used the ti-ba-ii calculator to get these results.<BR>\n" );
document.write( "similar results can be obtained from the arachnoid 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" );
document.write( "i also used excel to confirm that what i did was correct.<BR>\n" );
document.write( "here are the displays from the caclulator.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/051101.jpg\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/051102.jpg\"><BR>\n" );
document.write( "in the first calculator display, inputs were everything except present value.<BR>\n" );
document.write( "output was present value.<BR>\n" );
document.write( "in the second calculator display, the present value from the first calculator became the future value.<BR>\n" );
document.write( "inputs were everything except present value.<BR>\n" );
document.write( "output was present value.<BR>\n" );
document.write( "here are the displays from excel.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/051103.jpg\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/051104.jpg\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/051105.jpg\"><BR>\n" );
document.write( "in the excel displays, the first 11 months had zero investments.<BR>\n" );
document.write( "the last 48 months had investments of 7500 each.<BR>\n" );
document.write( "that took the 7500 investments from end of month 12 to end of month 59.<BR>\n" );
document.write( "this would be first investment at end of month 12 + 47 additional investments that stop at end of month 59.<BR>\n" );
document.write( "that was 11 months of no investments plus 48 months of 7500 investments.<BR>\n" );
document.write( "the present value of that cash flow was brought back to end of month 0.<BR>\n" );
document.write( "the present value of those cash flows confirmed the results from the financial calculator.<BR>\n" );
document.write( "the growth factor for each month was (1 + .105/12).<BR>\n" );
document.write( "the present value factor for each month was the cash flow for that month divided by (1 + .105/12) ^ (end of month).<BR>\n" );
document.write( "for example, the present value of 7500 invested at the end of the 12th month was 7500 / (1 + .105/12) ^ 12 = 6755.518547, as shown in the excel display.<BR>\n" );
document.write( "let me know if you have any questions.<BR>\n" );
document.write( "theo<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );