Jurisprudence is a big field of Islamic knowledge which has its own experts who spend decades of years to be able to study the evidence from Quranic verses after going through all the fields of Quranic studies, and the authentic Hadeeths after going through the fields of Hadeeth and Rijaal which deals with assessing the authenticity of every narration. We also have the principles of Fiqh which is logic of jurisprudential thinking. 
'You need to go through the evidence confirmed by the great jurisprudence scholars or Maraaji' of Taqleed to see the reasons of any Islamic rule including your question.

'In brief, Islam does not permit RIBA (usury) between Muslims, but not every interest known today is usury. When non Muslims keep your money and put is their business and give you whatever they everyone else from their profit, it is permissible for you to accept it. This is according to the jurisprudence evidence which has details in jurisprudence books written by the Maraaje' of Taqleed. You are accepting what they usually give to every one who keeps his money with them as part of their business.

'Wassalam.