In a complicated plan to end its financial problems, Capital Mortgage Investments of Chevy Chase has agreed to merge with The Columbia Corp., owner of controlling interest in Friendship Savings and Loan in Chevy Chase.

Capital Mortgage will become a wholly owned subsidiary of Columbia, which also plans to buy out minority shareholders in Friendship Savings.

Organized in 1969 as a real estate investment trust, Capital Mortgage decided to "de-REIT" two years ago after it had problems repaying lenders.

The merger plan -- requiring approval of Capital Mortgage shareholders, Maryland financial regulators, federal agencies and seven lenders -- was explained this way by John D. Wolf, vice president and treasurer.

First, owners of Capital Mortgages preferred stock -- about 22 percent of its shares -- would convert their shares into common stock. The preferred shares are owned by a group of banks, which took the stock in lieu of cash when Capital could not pay the full interest charges on loans.

Than all of Capital's shares would be exchanged on a one-for-one basis, for shares of Columbia Corp. That would make Capital's stockholders owners of more than 50 percent of the stock of Columbia.

Columbia then would purchase shares from minority stockholders of Friendship Savings, gaining whole ownership of the S&L.

Capital Mortgage Chairman William Damas and President Richard Kohr are already directors of Friendship and board members of Columbia. The composition of Columbia's board has not been determined.

The next step in the transaction would be for Capital Mortgage to transfer to Columbia $9.5 million worth of residential mortgages, in exchange for Columbia assuming an equal amount of Capital Mortgage's debt.

The mortgages involved in the swap were obtained by Capital after the collapse of some homebuilders for whom it was providing construction financing. Capital completed the projects and financed the homes.

Columbia, in turn, would transfer the $9.5 million in mortgages to Friendship Savings in return for approximately $7,125,000 of Friendship certificates of deposit.

Wolf said Capital's seven bank lenders tentatively have agreed to accept the Friendship certificates as payment for $9.5 million of Capital's debts. The discount, he explained, is because the banks consider the certificates better security than the mortgages which now secure the loans.

The rest of Capital's debts -- another $20 million -- are to be repaid over five years under a new loan agreement requiring, among other things, that Capital put up its remaining real estate assets as collateral.

Capital has assets of about $41 million, and in addition to its $29 million bank debt, owes $12 million to debenture holders. The status of the debenture holders would not be changed by the merger, Wolf said.

Under the merger plan, Columbia and Capital would share the $2.3 million gain resulting from the banks taking a writedown on the debt owed them.

Since it reorganized and gave up REIT status -- which provides tax advantages but limits business activities -- Capital Mortgage has retained ownership of several tracts of undeveloped land that now probably will be developed, Wolf said.