Dr. Monzer Kahf, a prominent economist and counselor states:

  1. The contract that generates interest is not valid according to Shari’ah as the Qur’an reads in Surah al Rum “it does not increase according to God.”  Hence the idea that interest earned is not ours because the contract that brought it does not produce any effect. It is still owned by the bank who paid it. In principle, it should be returned to owner but since the owner is a Riba practitioner we don’t do that, instead we give it to Muslim charity. This is in analogy to money whose owner is not known. It is not Haram for the charity but Haram for you.
  2. The only way to calculate it is to make use of all info sources that one has, depending on the case. If these were from accounts that are left aside, one can easily know the principals. But if there were movement of money in and out, it becomes more complicated. Banks usually give an accumulated figure of interest paid at the end of each year. Whatever part that you cannot calculate you should make an educated guess about it. Support that by a little extra and Istighfar and asking forgiveness from God. That includes all the past from the beginning of the accounts. In the example of the Prophet, pbuh, his uncle al Abbas was a practitioner of Riba before Islam and the Prophet, pbuh, on behalf of his uncle gave up the principal and interest all together (as mentioned in the famous farewell speech he gave in Arafat)

As a principle, this Haram money can be given to any poor/needy persons from the kind that deserve Zakah. Beggars are usually excluded because it has become a public knowledge that most beggars are professional but not really poor. It is preferred to give it to Muslim poor because there are much more of them than non-Muslim poor and they have little resource for help for them. I suggest that the best way is to give it to a trustworthy dependable Muslim charitable organization because these organizations are working in helping the poor and needy and they have better ability to give it to the right persons. It is not Haram to give it to poor non-Muslims or to give it to persons you know they are in need.”