For Alan Hardester, the 20 percent interest offered by Suburban Bank on its new floating rate insured savings account was just too good to pass up.

So Hardester, an executive of rival Fairfax Savings in Baltimore, marched next door to the competition's office and deposited some of Fairfax Savings' money in a Suburban account.

"It seemed like a good investment," said Hardester, who will be able to earn the 20 percent rate until Dec. 31 under a special Suburban incentive to get new deposits.

Suburban's rate is apparently the highest being offered locally on the new high-yield, insured money market accounts that were permitted yesterday for the first time by federal regulators.

The new account was created to compete with money market mutual funds, which have about $230 billion in assets. It was not clear yesterday how much money was coming out of the funds. No significant numbers of wire transfers out of their accounts were reported by T. Rowe Price and Dreyfus, two leading money market funds.

Interest rates offered by institutions offering the new account surveyed yesterday ranged from 7.5 to 20 percent, but rate competition here has been less intense than in some other regions.

Those institutions paying the highest interest or offering cash bonuses for new deposits appeared to be doing a land-office business on the first day of the new era in banking, which began with yesterday's introduction of the floating rate insured account.

There was a moderate-to-heavy response by depositors in the greater Washington area, according to reports received from 16 banks and savings and loans.

But for every person opening an account, there were many more shopping around, weighing offers.

Some economists have predicted that a rate war will cut into institutions' profits or at least raise their costs of funds. At Providence Savings and Loan in Vienna, Dick Tubbs, vice president for marketing, exclaimed, "Our greatest single expense may be the cost of coffee for the people waiting in the lobby." Providence, which is guaranteeing a 14.06 percent rate until Jan. 10, opened 800 new accounts, totaling $6 million. The average depositor put in $7,500, three times the minimum deposit required by law.

Most customers made deposits well in excess of the minimum, banks and savings associations reported. The average at United Savings and Loan of Vienna was more than $10,000. Security National Bank, offering 9 percent, reported the average new account totaled $18,000, but noted the average was increased considerably by one deposit of $100,000. Home Federal Savings and Loan, now paying 11.07 percent, also claimed a new $100,000 account.

American Security Bank, where the rate is 15 percent until Dec. 21, reported an average of $14,000 in the 270 accounts, totaling $5 million, it established on the first day. Gary Fleming, senior vice president, reported affluent customers waiting for the doors of the Spring Valley branch to open, whereas activity at the downtown office was negligible.

Columbia First Federal Savings and Loan said response was heavier in the suburbs than in the city. Independence Federal Savings and Loan, Women's National Bank and First American Bank of Virginia, all paying rates under 10 percent, mentioned slight-to-moderate activity.

Capital Bank in the District lured "many new customers" with a bonus of $50, even though it was paying just 8.77 percent interest.

In Maryland, several institutions that had achieved a head start in the contest for customers by offering retail repurchase agreements reported yesterday on the results. Baltimore Federal Savings and Loan transferred 2,000 of the repo accounts, amounting to $35 million, into Money Market Deposit Accounts, paying 12 percent through Dec. 30. And it opened another 380 accounts, for $5.7 million yesterday.

Interstate Federal Savings and Loan reported a good portion of its $4 million taken in yesterday was shifted by customers from their seven-day notice accounts, which had a minimum balance of $20,000.