New All Savers certificates will carry an annual rate of 12.14 percent starting Monday, based on results of a Treasury auction yesterday -- a day in which the new tax-free savings instruments attracted brisk though not overwhelming interest at banks, savings and loan associations and credit unions here and across the country.

Since the new rate will be lower than that currently applied, financial institution officials expect their offices and branches to be swamped with customers today and tomorrow. Many banks, S&Ls and credit unions have planned late hours today and an unusual full day of business on Saturday to cope with the anticipated boom.

Indeed, some industry experts are predicting such a rush to buy the newly authorized certificates that the Treasury will lose more in tax revenues than projected earlier as investors seek the tax-free interest advantage tied to the new deposits.

As of yesterday, when the one-year All Savers certificates were offered for the first time, the interest rate was 12.61 percent, based on the previous 52-week Treasury bill auction in early September. That rate will be in effect through the close of business Saturday.

Several bank and S&L officials said even though traffic in their branches wasn't as heavy as they had expected yesterday, inquiries poured into their offices about the new certificates. At Washington Federal Savings and Loan Association, "We've had people in line all day," reported President James L. Harris.

Much the same was reported by officials at First Federal Savings and Loan Association of Arlington, where 500 to 600 persons had signed up in advance for the new certificates.

American Security Bank provided each of its branches with 100 certificates yesterday and reported that several had sold them all by midday. But while traffic was brisk at Perpetual American Federal Savings and Loan Association, it was not as heavy as expected, said President William Sinclair.

"The initial response has been overwhelming," said Richard Lawton, president of Washington-Lee Federal Savings and Loan association in McLean.

Surveys by the U.S. League of Savings Associations showed that it was "busier than usual" at most of the 4,000 member associations.

Potential buyers of the certificates have been attracted by the relatively high interest rates -- compared with rates on regular passbook accounts -- as well as the tax-free advantage and, in many cases, heavy promotional campaigns that include cash and gifts as bonuses to certificate purchasers.

Interest on the certificates, which are sold in denominations as low as $100, is exempt from federal income taxes up to $1,000 for single taxpayers and $2,000 for joint returns. More than 15 states, including Maryland and Virginia, also have established the same exemption but the District will consider the interest to be taxable.

All Savers certificates may be sold from now until Dec. 31, 1982.

Government experts have projected that $65 billion to $70 billion would flow into depository institutions from the new certificates but savings and loan industry estimates run as high as $250 billion. It's not clear how much interest has developed in the certificates but a Treasury spokesman said yesterday the estimated loss in tax revenues due to the sale of All Savers is $500 million in fiscal 1982, $2.8 billion in fiscal 1983, and $1.9 billion in fiscal 1984. If All Savers deposits balloon to $250 billion, however, the tax loss would be several billions of dollars higher and that could complicate the administration's budget-balancing plans.

Legislation establishing the All Savers certificates swept through Congress with hardly a ripple, primarily as a result of heavy lobbying by the savings and loan industry. Spokesmen for the financially troubled S&Ls argued successfully that the certificates are the best vehicle for bringing badly needed mortgage funds into their associations. Seventy-five percent of the net new savings at financial institutions will be funneled ostensibly into housing or agricultural loans, but most housing experts have forecast few new mortgage loans. Instead, S&Ls will end up reducing the cost burden of current housing lending, these officials have predicted.

Money from All Savers certificates "offers the thrift industry finally, some type of stability to ensure the long term effect" rather than giving an immediate shot to housing, said Sinclair of Perpetual.

"We can have all the money in the world to lend and if interest rates remain high, people can't qualify to borrow at 18 percent," said Lawton, who is also president of the National Savings and Loan League.

Because of high interest rates, the new certificate "is a great stimulus for us to improve our position but we can't take money and loan it out at 13 to 14 percent," said Lawton.

Indeed, inflation and related "extraordinary levels of interest rates have created particular problems for those institutions whose portfolios are dominated by long-term, fixed-rate assets, such as residential mortgages," Federal Reserve Chairman Paul A. Volcker said yesterday.

Volcker made this point in urging a House subcommittee to approve emergency legislation that would give regulators clearer authority to deal with the problems of failing financial institutions.

Wide segments of the financial institutions industry opposed the legislation in testimony Wednesday. However, Volcker told a House subcommittee on financial institutions that although the bill won't cure the difficulty faced by some banks and S&Ls, it will "help manage a transitional problem."