Interest is paid on money because the person who has your money is using it for something else (usually to make even more money). So if they pay you 1% interest, they need to be making 2% interest somewhere else.

Not sure how this would work, as there is no mechanic in place where 'The Bank' can make 2% due to your deposit. No one really needs to borrow (and those who do are properly not safe to lend to). And there are no other investment opportunities for 'The Bank'. It would end up having to shift into a very large free market economic model (with bonds, securities, term deposits, etc.). Not sure that is the route that is intended for this world ^.^;

Fortunately there is an alternative! Invest that gil into items that you think will go up in value then sell when it does! Or, just spend it as Gil is plentiful and has no real value ^.^;