Butterfield Bank is paying the Carlyle Group a $4 million annual fee for advice on managing its balance sheet.The payment, which was revealed in the bank’s Annual Report 2010, is a three-year agreement that the bank entered into last October.According to Butterfield CEO Brad Kopp, the deal is already providing the bank with good value for money.Carlyle Group, a private-equity giant, was one of the lead investors in Butterfield’s $550 million capital raise last year. Carlyle invested $150 million at the time, holds about 18 percent of the voting power and has the right to designate two directors to the board.Mr Kopp said the arrangement had already helped the bank to improve its returns on investments, helped by Carlyle’s specialised analytical software and expertise.“We believe they’ve paid their fee already,” Mr Kopp said, after the first quarter brought an increase of $8.6 million, or 20 percent, in net interest income. “They have an interest in seeing us do well.”CFO Brad Rowse added: “It would be hard to find a consultant with interests more aligned with ours.” He added that two senior managers from Carlyle had been in Bermuda this week, working with the Butterfield team.