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Net profit in the first three months of the year climbed to 2.1 billion euros ($3.1 billion) from 1.8 billion in the same period of 2010, a statement said.
The result came within a few million euros of the bank's best ever quarterly result, in early 2007 before the global financial crisis erupted.
A major contributor to the results was the group's core investment bank activities, which reported a pre-tax profit of 2.6 billion euros, stable on the year.
Retail banking and asset management activities made considerable progress meanwhile, with a pre-tax result that leapt from 184 million euros a year ago to 978 million this time around.
The "record result" stemmed from the acquisitions last year of Postbank, which has Germany's largest retail banking network, and the private bank Sal Oppenheim.
Additional help was provided by the consolidation in Deutsche Bank's books of its 19.99 percent stake in Hua Xia Bank, a Chinese group, the statement said.
It quoted Deutsche Bank chairman Josef Ackermann as saying: "We will continue to invest in our franchise and are confident that we will deliver on our ambitious target of income before income tax of 10 billion euros from our business divisions."
Of that sum, 3.5 billion euros had already been earned in the first quarter, the bank said.
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