By Paul Lewis
BBC Radio 4's Money Box
Justin Urquhart Stewart says negative rates have been known
If the Bank of England cuts interest rates on Thursday could the interest paid on our savings fall below zero?
Negative interest rates, where the bank charges us to look after our savings, have been seen before.
In the 1970s Swiss banks charged foreign customers rather than paying them interest to hold their money.
But one economist said "it is not impossible but as close to that as you can get. Zero percent is a possibility for a brief period."
The problem faced by UK banks and building societies is that the recent Bank Rate cuts have left the interest paid to savers so low it cannot fall much further.
Rachel Thrussell, head of savings at comparison site MoneyFacts told BBC Radio 4's Money Box programme it was hard to see what would happen if the Bank of England did cut rates again, as is widely expected at its meeting on 8 January.
"It's getting to the point now with the straightforward accounts there is nowhere for them to go.
"There's a lot now paying 0.1%, 0.25%, 0.5%, so if base rate does go down again will they be able to pass this on to savers?"
Out of 256 instant access savings accounts listed by Moneysupermarket.com, 76 already pay less than 0.5% interest and 117 pay less than 1%.
Justin Urquhart Stewart, director of Seven Investment Management, says rates have been negative before.
"It does sound very strange, but it has happened in the past.
"If you go back more than 20 years to Switzerland, people were so worried about the value of currencies that they were running to anything they saw as a safe currency and the Swiss franc was it.
"So overseas investors had to pay for the privilege of holding Swiss francs - a negative interest rate."
A negative rate of -1% would mean that someone depositing £10,000 would get back just £9,900 at the end of the year, effectively paying the bank £100 for the privilege of holding their money for them.
Patrick Foley chief economist at Lloyds TSB said,
"It is not impossible but as close to that as you can get.
"Most banks and building societies will keep rates positive.
"Many savers are more concerned about the safety of their money than the interest earned.
"Zero percent is a possibility for a brief period if people feel their savings are safe and it is temporary.
"So you could see that briefly but I can't imagine them going negative."
BBC Radio 4's Money Box was broadcast on Saturday,
3 January 2009 at 1204 GMT.