Federal Realty Investment Trust, a Chevy Chase real estate trust organized in 1962, announced yesterday plans to acquire 15 shopping centers in a deal that would double that trust's assets from a current level of $40 million.

According to Steven Guttman, chief operating officer of the local REIT, Federal Realty has signed purchase agreements with Amterre Development Inc., to buy retail complexes in four states with more than 2 million square feet of commercial space.

Amterre, based in Bala Cynwyd, Pa., earlier announced plans to liquidare and the agreements with Federal Realty are subject to approval by Annterre's stockholders of that firm's entire liquidation plan.

For Federal Realty, which already owns 13 retail centers, the proposed agreement would represent its largest acquisition ever. With 28 community retail centers, Federal Realty would become one of the largest operators of shopping complexes in the mation.

Guttman said Federal Realty would invest $7 million to $8 million in cash to buy the centers and would raise these funds through bank loans. Federal Realty also would assume mortage debts and leasehold obligations of about $33 million.

Eight of the Amterre dhopping centers are located in the Philadelphia area and others are located in Petersburg, Va., New Jersey and Florida. Federal Realty's current shopping centers are located in the D.C area, Illinois, North Caroling, Michigan and Louisiana.About 80 percent of Federal Realty's current cash flow comes from shopping center properties.

In addition to Amterre stockholder approval, the Federal Realty deal is contingent on a review of data about the centers and agreements from such the centers and agreements from such third parties as companies that hold mortages on the centers. The centers range in size from 55,000 to 350,000 square feet.

In an industry that has suffered drom sharp setbacks caused by high interest rates, Federal Realty has been a standout - having paid a dividened in the second quarter that was its 63d consecutive quarterly payout. Dividends have been increased each year in the past 12 years. The equity trust's assets also have grown by $10 million in the first half of 1978.

During June, Federal Realty announced its third shopping center purchase in 1978 - the $4.5 million Bay Court Plaza with 28 stores in Dover, De.

Daniel Lyons, a managing trustee of Federal Realty, told analyst in New York recently that the trust's cash flow will exceed $2 million in 1978. Earnings of the Trust have increased at a rate of 32 percent annually over the past five years. Federal Realty has 1.43 million shares outstanding and more than $14 million in shareholder equity.