document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=241276>Question 241276</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The present value of an account earning 8 percent interest compounded monthly is $2400. An investor needs the account to be worth $4800 two years from now. How much must he contribute monthly?\r<BR>\n" );
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document.write( "i have worked on it and every time i get a wrong answer this is how i set up my problem:  FV=PV(1+i)^M </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #176727 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=176727\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you're using the wrong formula.\r<BR>\n" );
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document.write( "here's a list of the formulas you should use for the type of problems you will encounter mostly.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.algebra.com/algebra/homework/Finance/FINANCIAL-FORMULAS-101.lesson\" target = \"_blank\">LIST OF FINANCIAL FORMULAS</a>\r<BR>\n" );
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document.write( "The particular formula you are interested in is:\r<BR>\n" );
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document.write( "PAYMENT FOR A FUTURE VALUE<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+PMT%28FV%29+=+%28FV+%2F+%28%28%28%28%281%2Bi%29%5En-1%29%29%2Fi%29%29%29+ ALIGN=MIDDLE  ALT=\"+PMT%28FV%29+=+%28FV+%2F+%28%28%28%28%281%2Bi%29%5En-1%29%29%2Fi%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "PMT = Payment per time period<BR>\n" );
document.write( "FV = Future Value<BR>\n" );
document.write( "i = Interest Rate per Time Period<BR>\n" );
document.write( "n = Number of Time Periods\r<BR>\n" );
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document.write( "You do, however, have to make an adjustment.\r<BR>\n" );
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document.write( "You start off with $2400 and you want to end up with $4800.\r<BR>\n" );
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document.write( "The formula assumes the starting value is $0.\r<BR>\n" );
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document.write( "You need to subtract $2400 from the $4800 so that your starting value is $0 and your ending value is $2400.\r<BR>\n" );
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document.write( "You can then substitute in the formula as follows:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+PMT%28FV%29+=+%28FV+%2F+%28%28%28%28%281%2Bi%29%5En-1%29%29%2Fi%29%29%29+ ALIGN=MIDDLE  ALT=\"+PMT%28FV%29+=+%28FV+%2F+%28%28%28%28%281%2Bi%29%5En-1%29%29%2Fi%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where:\r<BR>\n" );
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document.write( "FV = future value = $2400<BR>\n" );
document.write( "i = .08/12 = .0066666667<BR>\n" );
document.write( "n = 2*12 = 24\r<BR>\n" );
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document.write( "Now you can use the formula as follows:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+PMT%28FV%29+=+%282400+%2F+%28%28%28%28%281.0066666667%29%5E24-1%29%29%2Fi%29%29%29+ ALIGN=MIDDLE  ALT=\"+PMT%28FV%29+=+%282400+%2F+%28%28%28%28%281.0066666667%29%5E24-1%29%29%2Fi%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This becomes\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+PMT%28FV%29+=+%282400+%2F+%28%28%28.172887932%29%2F.0066666667%29%29%29+ ALIGN=MIDDLE  ALT=\"+PMT%28FV%29+=+%282400+%2F+%28%28%28.172887932%29%2F.0066666667%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+PMT%28FV%29+=+%282400+%2F+%28%2825.93318978%29%29%29+ ALIGN=MIDDLE  ALT=\"+PMT%28FV%29+=+%282400+%2F+%28%2825.93318978%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+PMT%28FV%29+=+92.54549944+ ALIGN=MIDDLE  ALT=\"+PMT%28FV%29+=+92.54549944+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The future value of your payments will be $2400.\r<BR>\n" );
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document.write( "Add this to the $2400 that you started with and you will have $4800.\r<BR>\n" );
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document.write( "Because you were compounding monthly, your annual interest of 8% needed to be divided by 12 and converted to a straight rate before plugging into the formula.\r<BR>\n" );
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document.write( "8% / 12% = .666666667% / 100% = .0066666667.\r<BR>\n" );
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document.write( "Your number of years needed to be multiplied by 12 in order to get number of months because your payments were on a monthly basic and your compounding of interest was on a monthly basis.\r<BR>\n" );
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document.write( "That's why we multiplied 2 years by 12 to get 24 months.\r<BR>\n" );
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document.write( "Once everything was in sync, you could use the formula.\r<BR>\n" );
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document.write( "The formula you were using was not a payment formula.\r<BR>\n" );
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document.write( "It was a future value of a present amount formula.\r<BR>\n" );
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document.write( "You could not solve for payments using that formula.\r<BR>\n" );
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document.write( "you can confirm your answer is correct by plugging the value of the payment back into the original formula.\r<BR>\n" );
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document.write( "I used a financial calculator which is the easiest way if you know how to use it.\r<BR>\n" );
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document.write( "You can also used financial formulas in EXCEL if you know how to use them and you have a copy of EXCEL on your computer.\r<BR>\n" );
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document.write( "There are also financial calculators on the web that you can use to check your work if you know how to use them.\r<BR>\n" );
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document.write( "If you are interested in one, let me know and I'll scour the web for you.\r<BR>\n" );
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document.write( "They can help, but you do have to know how to use them based on the problems you have to solve.\r<BR>\n" );
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document.write( "Example is your problem.   If you didn't know that you had to subtract the present value to use the formula, you never would find the correct answer.\r<BR>\n" );
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document.write( "I MADE A MISTAKE.\r<BR>\n" );
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document.write( "I assumed the $2400 was NOT earning any money.\r<BR>\n" );
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document.write( "That changes the problem.\r<BR>\n" );
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document.write( "Big time.\r<BR>\n" );
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document.write( "Since the $2400 is invested also, then the problem changes as follows:\r<BR>\n" );
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document.write( "You first calculate the future value of the $2400 already invested in the account.\r<BR>\n" );
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document.write( "That comes out to be (using your original formula)\r<BR>\n" );
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document.write( "FV(PA) = $2400 * (1.006666667)^24 = $2814.931036\r<BR>\n" );
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document.write( "That's what $2400 earns in 2 years compounded monthly.\r<BR>\n" );
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document.write( "THAT's the amount you have to subtract from your $4800.\r<BR>\n" );
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document.write( "The result of that subtraction is what you need to make by plugging it into the payment for a future value formula.\r<BR>\n" );
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document.write( "$4800 - 2814.931036 = 1985.068964.\r<BR>\n" );
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document.write( "The payment formula becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+PMT%28FV%29+=+%281985.068964+%2F+%28%28%28%28%281.0066666667%29%5E24-1%29%29%2Fi%29%29%29+ ALIGN=MIDDLE  ALT=\"+PMT%28FV%29+=+%281985.068964+%2F+%28%28%28%28%281.0066666667%29%5E24-1%29%29%2Fi%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "PMT(FV) now comes out to be:\r<BR>\n" );
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document.write( "PMT(FV) = $76.54549949\r<BR>\n" );
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document.write( "You have $2400 in the account that earns you $2814.931036 by the end of 2 years.\r<BR>\n" );
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document.write( "You have payments of $76.54549949 per month that earn you $1985.068964 by the end of 2 years.\r<BR>\n" );
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document.write( "You add up $2814... and $1985... and you have $4800 at the end of 2 years.\r<BR>\n" );
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document.write( "To show you how this actually works in the account, I'm going to cut the number of months down to 5 because 24 months is too many months to show in such detail.\r<BR>\n" );
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document.write( "The future worth of $2400 at .0066666667 interest per month for 5 months is equal to $2481.073802<BR>\n" );
document.write( "The future worth of $76.54549949 payments for 5 months is equal to $387.8646645\r<BR>\n" );
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document.write( "Total future worth is $387.8646645 + $2481.073802 = $2868.938467\r<BR>\n" );
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document.write( "This is the money you will have in the account after 5 months.\r<BR>\n" );
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document.write( "Here's how it works:\r<BR>\n" );
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document.write( "all numbers truncated on display but full numbers used for calculations.\r<BR>\n" );
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document.write( "At end of month 1 you will have $2400 * 1.0067 + $76 = $2492.5<BR>\n" );
document.write( "At end of month 2 you will have $2492.5 * 1.0067 + $76 = $2585.7<BR>\n" );
document.write( "At end of month 3 you will have $2585.7 * 1.0067 + 76 = $2679.4<BR>\n" );
document.write( "At end of month 4 you will have $2679.4 * 1.0067 + 76 = $2773.9<BR>\n" );
document.write( "At end of month 5 you will have $2773.9 * 1.0067 + 76 = $2868.938466\r<BR>\n" );
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document.write( "The number calculated in detail after 5 months is the same number we calculated using the future value of present value formula and the payment for a future value formujla.\r<BR>\n" );
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document.write( "The same process applies to your problem except you carry it out 24 months instead of 5.\r<BR>\n" );
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document.write( "Sorry for the mistake but it was instructive so I left it in.  The mistake I made would be a common mistake if you didn't know better.  I should have.\r<BR>\n" );
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document.write( "You needed to break your problem into two parts.\r<BR>\n" );
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document.write( "The first part was the initial investment where you used the formula you started with.\r<BR>\n" );
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document.write( "You used this to calculate what the initial investment would be worth at the end of the 2 years.\r<BR>\n" );
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document.write( "You then subtracted that amount from $4800 so you could calculate how much payments you needed to make each month to come up with the difference.\r<BR>\n" );
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document.write( "At the end, the sum of the future value of your initial investment plus the sum of the future value of the payments needed to be equal to $4800.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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