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Math Help - Formula for FVoAD with continuous compounding

  1. #1
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    Formula for FVoAD with continuous compounding

    I gather that future value of ordinary annuity with continuous compounding of interest is calculated as

    FV = PMT [e^rt -1]/[e^r-1]

    So to find future value of an annuity due with continuous compounding of interest I would multiply the former by an extra interest factor of e^r thus making the formula as

    FV = PMT e^r [e^rt -1]/[e^r-1]

    Is this correct, the reason I think this may work is since for discrete compounding of interest we multiply the interest factor of (1+i) to the future value of annuity formula as

    FV = PMT (1+i) [(1+i)^n - 1]/i

    Just a confirmation of the correctness of the formula will suffice
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  2. #2
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    Re: Formula for FVoAD with continuous compounding

    \delta = continuously compounded rate
    i = annually compounded rate

    if you are still paying your annuities as annually, rather than continuously, then all you need to do is convert your "continuously compounded" interest rate into a normal one and then use the standard formula.

    if you note that e^\delta = 1+i you will see whether or not you have the right answer.


    More often the calculation of interest is the value of annuity paid continuously, which is a different concept to what you described above.
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