With interest rates at a record low, the head of RBS has warned savers to research "alternative" options to keeping their money in a bank deposit account.
Ross McEwan, Chief Executive of RBS, told ITV News: "My advice to savers is get some good advice from financial professionals as to where they should be putting their money."
This has sparked fears from customers that the cut could lead to banks effectively closing their doors to savers.
Investing £3,500 in an easy-access cash savings account with an average current rate of 0.55% would only earn £19.25 a year.
An easy-access cash ISA with an average return of 0.94% earns £32.90 in annual interest.
Over 10 years, the average annual return on a typical UK stocks and shares ISA is 5.5% a year, earning £192.50 in interest.
RBS customer Simone Clark told ITV News: "The percentage that you earn is so small that I could put it in a piggy bank - I won't earn anything - but the interest is so little anyway, it makes no difference."
Financial commentator Iain Martin warned that low interest rates could have an adverse effect on people's saving habits.
The danger from having interest rates too low for too long is that people get out of the savings habit, they can't make any return from saving, and they're forced into financial speculation and gambling too much on the stock market or expecting too much from property.