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calculate future value with recurring deposits
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using the following values: the formula for the future value of an annuity due is d*(((1 + i)^t - 1)/i)*(1 + i) see calculating the present and future value of annuities in an annuity due, a deposit is made at the beginning of a period and the interest is received at the end of the period.  this is in contrast to an ordinary  annuity, where a payment is made at the end of a period. the formula is derived, by induction , from the summation of the future values of every deposit.  the initial value, with interest accumulated for all periods, can simply be added. so the overall formula is
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