document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=423416>Question 423416</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am 30 years old and want to retire at age 60. I want to be able to collect $60,000 a year for 20 years. At 5% interest, how much money do I need to invest today to be able to collect $60,000 for 20 years by the time I reach 60?\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you in advance for any help and/or consideration. This one is really stumping me because I do not even know what formula to use.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #295337 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=295337\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you will be retiring in 30 years (60 - 30 = 30)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you want to be able to collect $60,000 a year for 20 years.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since you normally collect the money monthly, i'll assume the following:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5% per year compounded monthly is equivalent to .416666667% per month.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "$60,000 per year is equivalent to $5,000 a month.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since you want to collect for 20 years, that's equivalent to 240 months.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the present value of $5,000 monthly at .4166666667% per month for 240 months is equal to $757,626.5654\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That's the amount of money you would need to have in the account at the beginning of your retirement period.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in order to have that much money in your account 30 years from now, you would need to invest $169,576.9749 today at 5% annual interest compounded monthly.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formulas you will need at the present value of a payment formula.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is also called the present value of an annuity.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you also need the present value of a future amount formula.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formulas you require are shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "PRESENT VALUE OF A PAYMENT<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+PV%28PMT%29+=+%28PMT+%2A+%281+-+%281+%2F+%281%2Bi%29%5En%29%29%2Fi%29+ ALIGN=MIDDLE  ALT=\"+PV%28PMT%29+=+%28PMT+%2A+%281+-+%281+%2F+%281%2Bi%29%5En%29%29%2Fi%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "PV = Present Value<BR>\n" );
document.write( "PMT = Payment per time period<BR>\n" );
document.write( "i = Interest Rate per Time Period<BR>\n" );
document.write( "n = Number of Time Periods\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "PRESENT VALUE OF A FUTURE AMOUNT<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PV%28FA%29+=+FA+%2F+%28%281%2Bi%29%5En%29+ ALIGN=MIDDLE  ALT=\"PV%28FA%29+=+FA+%2F+%28%281%2Bi%29%5En%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "PV = Present Value<BR>\n" );
document.write( "FA = future amount<BR>\n" );
document.write( "i = Interest Rate per Time Period<BR>\n" );
document.write( "n = Number of Time Periods\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since you will be compounding monthly, you need to make some adustments to the number of time periods and the interest rate per time period.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for the present value of a payment formula:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i = .05 / 12 = .004166667<BR>\n" );
document.write( "n = 20 * 12 = 240<BR>\n" );
document.write( "pmt = 60000 / 12 = 5000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for the present value of a future amount formula:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i = .05 / 12 = .004166667<BR>\n" );
document.write( "n = 30 * 12 = 360\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the present value of a payment formula will get you to $757,626.5654\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's the amount you have to have in the account 30 years from now.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the present value of a future amount formula will get you to $169,576.9749.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's the amount you will need to invest today.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "some references you might find useful are shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.algebra.com/algebra/homework/Finance/FINANCIAL-FORMULAS-101.lesson\" target = \"_blank\">http://www.algebra.com/algebra/homework/Finance/FINANCIAL-FORMULAS-101.lesson</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );