The contribution is the amount that, added at the end of each month, makes the balance reach the goal on time. At a zero rate, it is the gap between the goal and the current amount, divided by the months.
Contribution = (goal − current × (1 + i)ⁿ) × i ÷ ((1 + i)ⁿ − 1)
To reach 10,000 in 12 months, starting from zero at 1% a month, the contribution is 788.49. At a zero rate, a goal of 12,000 in 12 months needs 1,000 a month. If the current amount alone already passes the goal, the contribution is zero.