Why is banking something Muslims are allowed to do?

They can, as long as it does not imposed interest for loans.

Explanation:

Muslim teachings prohibited the followers to lend money with  a 'Riba'. Riba refers to any additional amount of money that is asked beyond the original amount loaned to other people. They considered this as unethical.

This is why Banks in Muslim countries usually implemented a sharia-compliant finance. These banks would not impose interest rates to the customers who ask for the loans.

They obtain their profit to a method that they refer to as 'Mudarabah'  or profit sharing. If the Bank loan a certain amount of money to a businesses, the bank inquire the business to share some part of the income that they generated from the loan.

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