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Al Rayan bank offers the best rate for three-year bonds, according to a report by Moneyfacts, with 2.3%. BLME, another Islamic lender, has the best rate on 2-year bonds, offering 2%.
French lender RCI has the best rate on an easy-access account with 1.45%
It is likely to get worse for savers. The Bank of England is pondering another rate cut to counter the economic risks of Brexit and stimulate lending at the expense of savers.
"Savers have been fighting an uphill battle to get a decent return in the first half of this year," Charlotte Nelson, finance expert at Moneyfacts, said.
"Indeed, over 900 individual cuts to savings rates have occurred since January, which is shocking considering that there have only been 111 rate increases over the same period. As a result, it's not surprising that many have begun to wonder if the cuts will ever end."
According to a survey in the Financial Times, markets "have already priced in a 75% chance of interest rates being cut from 0.5% to 0.25% this week."
Britain's interest rates have been at a historic low of 0.5% since March 2009 and before Britain voted to leave the European Union on June 23, the BOE was priming itself to eventually start raising rates again.
Here is how that has affected saving rates, according to Moneyfacts:
Moneyfacts