With nine days to go until the debut of new federally insured money market deposit accounts, banks and savings institutions around the country are scrambling to pull in customers ahead of time.

To get their share of the estimated $100 billion expected to flow into the new accounts, banks and S&Ls are offering bonuses, high interest rates and premiums ranging from the usual toasters and television sets to "E.T." dolls.

A new era in banking will begin Dec. 14 when financial institutions can at last pay as high an interest rate as they wish on short-term insured deposits.

Individual banks in the Washington area haven't yet revealed their rates, which will vary as interest rates go up and down. Initially most rates are expected to be in the 8.5 to 9.5 percent range, though some institutions plan to offer higher rates at first to entice customers.

Federal regulations require a minimum deposit of $2,500 for the insured money market savings account. Funds can be withdrawn at any time without penalty, but if the balance falls below $2,500 the interest rate is reduced to 5 1/4 percent. Transfers are limited to six per month.

The new accounts are expected to draw billions of dollars of deposits. The big question is where that money will come from.

Economists are watching to see how much of it comes from rival money market mutual funds, which have $231 billion in assets, and how much will simply be shifted from existing low-interest and passbook accounts that now hold $347 billion in savings.

If many customers elect to shift their low yielding funds to the new account, it could dramatically increase institutions' cost of funds. This could mean higher loan rates or poorer profits for the banks.

Washington area banks and savings associations are not expected to be as aggressive as financial institutions in other parts of the country in bidding for the new accounts. Local institutions have a reputation for what one banker called "bland product development" and are not eager to pay higher interest rates.

Financial institutions in some parts of the country badly need more deposits and are rushing to get them.

First out of the gate was Continental Illinois National Bank in Chicago, which began bidding for the new business on the same day that federal regulators laid down the final rules. Continental Illinois said it would pay depositors 10 percent interest on their money until the new accounts become legal. Until Dec. 13 Continental Illinois will put the funds in an "bridge account" utilizing an uninsured repurchase agreement called a "repo."

Home Federal Savings and Loan in San Diego set a $5,000 minimum deposit in exchange for a bonus of three points above the average money market rate during the first six months. The S&L reportedly opened 11,000 accounts with $125 million after the offer appeared.

Biscayne Federal Savings and Loan of Miami proposed paying a dollar a day bonus until Dec. 14 for accounts up to $4,999 and $2 for accounts over that. It opened 300 accounts the first day.

New York City savings banks, among the most aggressive marketers in the nation, jumped in with bonuses, and the city's commercial banks jumped in without such incentives. Citibank set a $5,000 minimum, but Chase Manhattan offered a bonus of 1 percent of the balance plus a 10 percent rate guaranteed for a month.

East New York Savings Bank proposed a 9.55 percent annual percentage rate through Jan. 11 on $2,500 deposits and 11.74 on $5,000 or more. It pledged to always pay one quarter percentage point more than the weekly average of money market funds that invest in U.S. government and agency securities. (This rate tends to be lower than the overall average of money market funds.)

Dime Savings Bank promises a 15 percent "bridge" repo plus a 10 percent annual yield for one year plus a cash bonus ranging from $12.50 for a $2,500 deposit to $500 for $100,000. (All rates are given in annual yields; i.e., the percent interest that would be paid if the bonus offer lasted a full 12 months. For example, a 15 percent annual rate on $2,500 for 10 days amounts to $10.40, or $6.75 more than the same balance would earn at passbook rates.)

Central Federal Savings Bank in New York upped the ante to 3 percentage points above the money market fund rate for three months, provided the account is opened by Dec. 13. For charter investors, the New York Bank for Savings proposed a repo paying 10 percent plus a 10 percent bonus on the interest paid for the next six months.

Thus far, the only institution in this region to advertise an introductory incentive is believed to be Baltimore Federal Savings and Loan. On Wednesday, it announced a bridge repo paying 12 percent on $2,500 accounts until Dec. 13. Vice President John Moran said the S&L was seeking to repeat its 1981 tactic when it attracted "substantial deposits" by offering advance repos linked to All Savers accounts.

For some time a number of Maryland S&Ls, insured by the Maryland Savings Share Insurance Corp., have been advertising accounts similar to the money market deposit account and paying 10 to 11 percent.

Federally insured financial institutions in metropolitan Washington are expected to begin advertising this week. Telephone interviews with executives of a half dozen banks and savings and loans indicate that most plan to index their rates to short-term Treasury bill yields, currently about 8 1/2 percent. Another possibility is to tie the rate of the new account to Donoghue's Money Market Fund index, averaging 8.3 percent this week. Five out of six local institutions will stick with the $2,500 minimum; one plans to require a higher minimum and to include other services in a package deal.

William Sinclair, president of Perpetual American Federal Savings, expressed surprised at the "laid back" attitude of bankers here compared with their colleagues elsewhere. Some are waiting to see what their competition will invent; others are waiting for final instructions due Monday on the number of telephone transfers permitted with the new account.

Although Washington institutions do not usually go in for wild promotion schemes, Sinclair said he would not be surprised to see some here propose one-month introductory interest rates of between 16 and 18 percent.

Even though balances in the new account are insured up to $100,000 and money market funds are not, Sinclair observed that the existence of insurance would not compensate for lower rates. "We will have to do better on rates than the money market funds to win back dollars," he said.