bank account

Using halaal money from an account that accrues interest

Q: I have some fixed deposits which accrues some interest. Now if I perform Hajj/Umrah from the halal money i.e. not earned from the interest, will it be accepted? I ask this, because I heard that the prayers of the one who deals with riba are not accepted. I'd also like to know if my other prayers, i.e., Salah, Fasting etc, are accepted as well?