Praise be to Allah.
If this amount reaches the nisaab (minimum threshold) and one full hijri year has passed, then zakaah must be paid on it, whether it is for savings or otherwise. The nisaab is whatever is equivalent to 85 grams of gold or 595 grams of silver. The amount that must be paid is 2.5% of the money.
See question no. 2795.
If the amount of money decreases and drops below the nisaab during the year, then no zakaah is due, and you start reckoning the year anew when the amount of money reaches the nisaab again.
If the amount of money increases gradually, then the matter is subject to further discussion.
1 – If the new money comes from the first money, such as profits on the saved money in an Islamic bank – then zakaah must be paid on the whole amount when one year has passed since the original money was acquired, even if only a few days have passed since the profit was acquired. Hence the fuqaha’ said that the year for the profits is the same as the year for the original amount.
2 – If the extra money does not stem from the original and is separate money, such as money that a person saves from his salary, then the basic principle is that a separate year should be calculated for each amount of money. It is not necessary for this new money to reach the nisaab, because the nisaab has already been reached by the first amount of money.
Based on this, then whatever you save during Ramadaan, you should pay zakaah on it the following Ramadaan, and whatever you save in Shawwaal you should pay zakaah on it the following Shawwaal, and so on.
Undoubtedly it is difficult for a person to make a separate account for his savings each month, and to pay zakaah on every amount he saves when one year has passed since acquiring it. Hence it is easier for him to pay zakaah on all his saving during the year when one year has passed since his money first reached the nisaab.
In that case, you will be paying zakaah on money for which one year has not yet passed, but there is nothing wrong with that, because it comes under the heading of paying zakaah in advance before one year has passed.
We have discussed that previously in the answer to question no. 26113, where we have quoted the fatwa of the Standing Committee concerning that, which we will repeat here because it is useful:
With regard to a person who owns money that reaches the nisaab then acquires other money at different times which does not stem from the first amount of money, and is rather separate from it, such as the salary that is paid monthly to an employee, or an inheritance, gift or rent paid on property, etc,
if he insists on having all his rights and on not giving any charity to those who deserve it apart from what he is obliged to give, then he should make a schedule of his earnings and write down every amount and the date on which he took possession of it. Then he should pay zakaah for each amount separately when one year has passed from the date on which he took possession of it.
But if he wants an easier method, and wants to be more generous and give precedence to the poor and others who are entitled to zakaah over himself, then he can pay zakaah on all the money he possesses when one year has passed from the date when his wealth first reached the nisaab. This will bring a greater reward and raise him higher in status; it is easier for him and is more generous towards the poor and needy and others who are entitled to zakaah. Whatever extra amount he may pay will be regarded as a “down payment” on the zakaah for any wealth for which one year has not yet passed.
(From Fataawa al-Lajnah al-Daa’imah, 9/280).
And Allaah knows best.