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Thread: How to calculate future value with a monthly payment?

  1. #1
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    How to calculate future value with a monthly payment?

    So I went to the investor.gov website and got to playing around with one of their compound interest calculators and entered the following: A =$1000, PMT=$150(monthly), t=45 years, r=8%, and it's being compounded monthly. The calculator said the future value would be $827,344.58 I would like to know what formula was used to get this result and how does the calculator know when I will make my deposit? Beginning of the month or end of the month? Any help figuring out how the calculator got this answer would be appreciated! Thanks!
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  2. #2
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    Re: How to calculate future value with a monthly payment?

    What you have here is equivalent to a savings account that'll look like this:
    Code:
    MTH     AMOUNT     INTEREST       BALANCE
      0                             1000.00
      1     150.00         6.67     1156.67
      2     150.00         7.71     1314.38
      3     150.00         8.76     1473.14
    ....
    538     150.00      5403.81   816125.64
    539     150.00      5440.84   821716.48
    540     150.00      5478.10   827344.58
    Interest calculated this way (month 3 as example):
    1314.38 * .08 / 12 = 8.76

    I'm watching a football game...so I'll let someone else
    give you the 2 formulas required!!!
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  3. #3
    Member Walagaster's Avatar
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    Re: How to calculate future value with a monthly payment?

    The formula is$$
    FV =P\left(\frac{(1+r)^n-1}{r}\right)+ A(1+r)^n$$
    where $P=150,~r=\frac{.08}{12},~A=1000,~n=45*12 = 540$.
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  4. #4
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    Re: How to calculate future value with a monthly payment?

    Thanks!!
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  5. #5
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    Re: How to calculate future value with a monthly payment?

    Thanks for the formulas!!!
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  6. #6
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    Re: How to calculate future value with a monthly payment?

    If (as example) you wanted to know what the monthly deposits
    contribute to the 827344.58, you'd simply deduct the future
    value of the initial $1000:
    827344.58 - 1000*(1 + .08/12)^540
    = 827344.58 - 36163.60
    = 791180.98

    On your "beginning or end of month" question,
    the calculator simply needs to be able to do both,
    and should contain a "button!" labelled "immediate or deferred?"

    YOKAY?
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