T. Rowe Price Associates, a giant mutual fund company that is based in Baltimore, announced yesterday that it will sell 1.25 million shares of stock to the public at prices ranging from $21 to $24 a share.

The investment company operates 17 mutual funds with assets of about $19.8 billion.

George J. Collins, president and chief executive officer of Price, said last fall that his firm was thinking about going public because of increasing competition in the investment management business and the "rising cost of providing investment services."

T. Rowe Price Associates, which was formed in 1937, is owned by its employes. The firm's decision to go public, at a time when the stock market is at new heights, coincides with similar decisions made recently by a number of top brokerage firms. These firms include Morgan Stanley & Co., Bear Stearns & Co., L. F. Rothschild, Unterberg, Towbin and Alex. Brown & Sons of Baltimore.

Of the Price shares to be sold, 855,200 will be offered by the company, while 394,800 will come from a group of present and former employes. The shares to be sold represent 18 percent of the company's 6.9 million outstanding shares.

The offering will raise about $19.2 million for the company and $8.9 million for the selling shareholders, at an estimated $22.50 sales price.

The firm's share of the funds raised will be used to acquire certain stock "rights" still held by former employes who gave up their stock when they left the firm. The distribution formula was not specified.

The selling shareholders include two present executives, Carter O. Hoffman, senior vice president, who is selling 105,000 shares and retaining 179,707 shares, and Austin H. George, vice president, who is selling 18,200 shares and retaining 76,170 shares. Curran W. Harvey, former president and chief executive officer, will sell 175,000 shares and keep 185,362.