New Orleans-based First NBC Bank Holding Co.’s $51 million acquisition of Metairie-based State Investors Bancorp Inc. will take longer to complete than originally expected.

The companies have extended their merger agreement’s expiration date from Aug. 30 to Dec. 31. Under the extension, First NBC will pay State Investors’ shareholders an additional fee over the original $21.25 per share. The fee is 5 percent a year, or about three-tenths of a cent per.

The merger has already been approved by the boards of both companies, State Investors shareholders and state regulators. Federal approval is still required.