document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203594>Question 203594</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the algebra formula if I invest into an ordinary annuity where $1100 is deposited each year into an account that earns 4.8% interest compounded annually </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153617 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=153617\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> YOUR IMMEDIATE CONCERN<BR>\n" );
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document.write( "Your question was:<BR>\n" );
document.write( "What is the algebra formula if I invest into an ordinary annuity where $1100 is deposited each year into an account that earns 4.8% interest compounded annually<BR>\n" );
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document.write( "Since you are given a payment, then the formula you are looking for is either PRESENT VALUE OF A PAYMENT or FUTURE VALUE OF A PAYMENT.<BR>\n" );
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document.write( "PAYMENT and ANNUITY mean the same thing as far as the formulas are concerned.  The annuity is a form of payment.<BR>\n" );
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document.write( "Some formulas might use the term WORTH rather than VALUE.  They also mean the same thing.<BR>\n" );
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document.write( "PRESENT VALUE OF A PAYMENT will give you the value of an annuity at the present time which would normally be the account you are withdrawing from.  It is also the amount of money you would have to invest now in order to be able to withdraw a certain amount of money for a specified period of time in the future.<BR>\n" );
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document.write( "FUTURE VALUE OF A PAYMENT will give you the value of an annuity in the future if you invest a certain amount of money into it over a specified period of time.<BR>\n" );
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document.write( "If you're dealing with retirement funds, you are usually investing in the fund while you are working and withdrawing from the fund after you've retired.  <BR>\n" );
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document.write( "If you're talking about a loan, the present value of the loan payments is the amount of the loan, and the future value of the payments is the amount of money being made by the lender.<BR>\n" );
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document.write( "What's missing in your question is the specified period of time.  The ordinary annuity formulas deal with a specified period of time.  <BR>\n" );
document.write( "There are other formulas that deal with perpetuity (forever) but those are not the ordinary formulas.<BR>\n" );
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document.write( "The formula for PRESENT VALUE OF A PAYMENT / ANNUITY is:<BR>\n" );
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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<BR>\n" );
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document.write( "the formula for FUTURE VALUE OF A PAYMENT / ANNUITY is:<BR>\n" );
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document.write( "FUTURE VALUE OF A PAYMENT<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+FV%28PMT%29+=+%28PMT+%2A+%28%281%2Bi%29%5En-1%29%2Fi%29+ ALIGN=MIDDLE  ALT=\"+FV%28PMT%29+=+%28PMT+%2A+%28%281%2Bi%29%5En-1%29%2Fi%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "FV = Future 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<BR>\n" );
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document.write( "You need the interest rate per time period, which can be given in years, months, quarters, whatever.  In your case, it looks like it's 4.8% per year which you need to convert from percent to rate by dividing by 100%.<BR>\n" );
document.write( "4.8% / 100% = .048 which is your interest rate per year.<BR>\n" );
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document.write( "You need the time period which can also be given in years, months, quarters, whatever.  In your particular case it will be years.  It's the part that's missing in your question.<BR>\n" );
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document.write( "Your payment is $1100 per year. <BR>\n" );
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document.write( "The only other thing you would need to know is if the payments are being made at the end of the year or at the beginning of the year.  The ordinary annuity formulas assume end of year payments.   If beginning of the year payments, then an adjustment to the formulas is required.  The tutorials cover that.  You should just doublecheck whether they are talking about end of year payments or beginning of year payments.<BR>\n" );
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document.write( "If you need more information, the lessons are instructive. <BR>\n" );
document.write( "In order to find them, go to www.algebra.com, scan to the bottom of the page.<BR>\n" );
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document.write( " on the right you should see a highlighted word called \"lessons\".  click on it (it's a hyperlink) and look for my lessons on financial formulas.  just do a find on this page for \"theo\" and they'll be highlighted, if you can't find them by just scanning.<BR>\n" );
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document.write( "when you scan to the bottom of the algebra.com home page, you will see something that looks like the following:<BR>\n" );
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document.write( "Our 981  algebra tutors  solved 141111 problems submitted by 37355 registered students, wrote 416 lessons, 172 solvers, to be seen by thousands! They become famous and promote their math sites. Click here to learn about algebra tutoring and how to promote your math website or a book. Watch it happening with a realtime Algebra.Com ticker. <BR>\n" );
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document.write( "you can see right now that there are over 416 lessons written.  those numbers will change over time, but you are in the right section.  lessons is not highlighted here as a hyperlink, but will be on the algebra.com home page.<BR>\n" );
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document.write( "the lessons I have written covering the topic of financial formula, of which annuities is a part of, even though I don't call them annuities, but payments, are as follows:<BR>\n" );
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document.write( "Basic Formulas and Assumptions used in Financial Formulas<BR>\n" );
document.write( "Future Value of a Present Amount<BR>\n" );
document.write( "Present Value of a Future Amount<BR>\n" );
document.write( "Payment for a Future Value<BR>\n" );
document.write( "Payment for a Present Value<BR>\n" );
document.write( "Future Value of a Payment<BR>\n" );
document.write( "Present Value of a Payment<BR>\n" );
document.write( "The Relationship between Present Value, Future Value, and Payments<BR>\n" );
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