All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If this saving account is in an Islamic bank that abides by the Sharee’ah rulings in its financial transactions, then there is no harm on you to benefit from these profits.
However, if the saving account is in a Riba-based bank, then such profits are Riba (interest and/or usury) and the owner of the account is not permitted to benefit from them. Rather, he must dispose of them by giving them to the poor and needy unless the account holder himself is poor, in which case, there is no harm on him to benefit from this ill-gotten (forbidden) money according to his need.
An-Nawawi said:
“He may spend it (the unlawful money) on himself and his family if he is poor, because if his family is poor, then they meet this description (of being poor). In fact, they are more deserving to get it as charity than anyone else. And he himself can take (money) in proportion to his need because he is also poor.” [End of quote]
It should be noted that it is not permissible for a person to open a saving account in a Riba-based bank at all. If one must deal with a Riba-based bank because there are no Islamic banks in the place where he is, then he should open a current account, as this is a lesser evil.
For more benefit, please refer to Fataawa 294835, 265492, 289435 and 290329.
Allah knows best.