Madison National Bank, which has just come through a difficult economic year with a healthy 22 percent gain in earnings, already is projecting lower profits for this year because of the drain of paying interest on checking accounts for the first time.

At a meeting of securities analysts last week, Madison's chairman, K. Donald Menefee, said his bank expects net income to rise just 15 percent in 1981, primarily as the result of expenses related to NOW accounts.

He estimated that 70 percent of the new accounts represent conversions from noninterest-bearing checking accounts. He also said his bank may have lost some deposits in January, when customers withdrew funds to start NOWs elsewhere, but he emphasized it is too early to tell. A good number of people are said to be keeping their regular checking accounts until all checks clear before switching.

Madison is Washington's sixth-largest bank, with $174 million in assets. Last year its return on assets was 1 1/2 percent, a commendable figure compared with the industry average of about 1 percent. Madison is capitalized at about $15 million. Last year its return on equity was a high 18.7 percent. Since 1974 its compounded annual earnings increases amounted to 21.6 percent.

Menefee said Madison consistently has rebuffed attempts to acquire it during its 17 years of existence. The bank has but 900 shareholders, and 58 percent of the stock is controlled by the board.

The directors, some of whom are the original directors or their offspring, are said by analysts to be very loyal to the bank and unwilling to sell. Indeed, one estimated the average number of shares traded daily at 100, out of a total of 410,000 outstanding.

Another reason is the preponderance of insider loans made to Madison's board members. Four years ago, The Washington Post reported that all but one of the $100,000 or more real estate loans made by the bank over a three-year period went to directors, stockholders and former employes.

One of those was Dominic F. Antonelli, the parking garage magnate, who was later indicted for bribery and conspiracy for allegedly obtaining loans from Madison for mayoral aide Joseph P. Yeldell. Both men were acquitted of the charges.

Asked by an analyst about Madison's insider loans, Menefee replied that no one besides the newspaper had criticized the loans. The comptroller of the currency said the loans were not in themselves illegal and had caused no losses to the bank.

Menefee defended the deals. "Our board is very active around town [particulary in real estate.] These people could get loans from any bank in Washington. Some of them have complained they could even get better terms elsewhere.

"Moreover, they have substantive deposits with Madison, and the bulk of their loans are secured by real estate." In return for this loyalty, Madison capped all its loans last year at 15 1/2 percent, even when the prime was over 20 percent.

Menefee described Madison's policy as one of "being aggressive in the marketplace." Like its larger competitors, Madison is preparing for an expanded future by forming a holding company, James Madison Ltd. The proposal will be put to the stockholders at the annual meeting in late April. Two million shares will be authorized, but no new offering is planned. Instead, there will be a one-for-one swap with bank stock.

The principal reason District banks are establishing holding companies is to prepare for the day when the law is changed to permit them to acquire other banks in neighboring states.

Menefee also is looking forward to the day when the District "will become, if not the financial capital of the world, at least a highly rated international center."