If the details of its strategic agreement with CheckFree Corp. are any indication, Bank of America has very high hopes for electronic billing.

The companies said Monday that they had entered into an agreement whose planning was announced in April. CheckFree, which is based in Atlanta, got a 10-year contract. Bank of America, based in Charlotte, N.C., got 10 million shares of CheckFree stock — plus warrants to buy that many more if it is delivering more than 10 million electronic bills a month to more than 10 million of its customers through the CheckFree service.

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