First Women's Bank of Maryland, which opened for business late in 1979, operated profitably during its first full year in business and announced plans yesterday to lower its prime rate by 2 percentage points.

The Rockville-based bank reported 1980 earnings of $55,077 (46 cents a share) as assets rose to $9.9 million and deposits increased to $8.2 million by Dec. 31. Most businesses do not earn enough money to be profitable during an initial year in business, although Women's National Bank of Washington recorded a similar feat.

First Women's of Maryland, a state-chartered institution with 402 stockholders, announced that its prime rate starting today will be floating at 2 percentage points below the money center prime, which is the rate charged by banks for some of their major corporate customers.

Since the prime fell last week to 19 1/2 percent, the rate at First Women's today will be 17 1/2 percent. President Eve R. Grover indicated the lower prime will be maintained for an indefinite period, while most rates are at historically high levels.

Analysts at Commercial Credit Co. of Baltimore said Friday that the recent reduction of the prime rate partially reflects seasonal weakness of business loans at banks. Interest rates are likely to drift lower, but underlying market trends suggest that the decline may be limited, Commercial Credit said.