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The bank offered $40 million on Wednesday and said it had sold $37.6 million at a cut-off price of 7.1401 pounds per dollar, unchanged from its last sale on Monday.
The rates at which banks are allowed to trade dollars are determined by the results of central bank sales, giving the bank effective control over official exchange rates.
In the unofficial market, the pound was trading at 7.67 to the dollar, one trader said, weaker than Monday's rate of 7.64 to the dollar.