Sharia does not allow Interest, IIRC.
Hey who wants a bank that pays interest?
On the other hand, if the bank will give me a mortgage and not charge me interest, then I might be in favor.
Sharia forbids "riba" which is usury. The fundamental concept is the unjust interest charge on business transactions. Not all Islamic scholars agree on what "riba" happens to be and how/when punishment for such is meted out. There are banks in Islam and they charge interest.