This year in banking promises to be one of intense competition, industry consolidation and inventive communications.

The advent of interest on checking accounts nationwide, plus a wide range of new asset powers for thrift institutions such as credit cards and small-business loans, will spawn intramural competition as never before among depository institutions. These, in turn, feel threatened by the increasing number of bank-like services offered by money market funds, broker/dealers, finance, insurance, credit card and television companies, and even retailers.

Not only do they unsurp traditional bank functions, they can usually offer more favorable terms because they are not subject to the same restrictions. For example, Merrill Lynch's Cash Management Account is, in effect, a checking account that pays market interest rates. Sears Roebuck plans to offer obligation notes directly to the public. And, thanks to increasingly sophisticated telecommunications, that familiar fiction Anybank, Anytown, U.S.A. is becoming a reality.

While banks and thrift institutions are still trying to absorb the shocks of deregulation and universal reserve requirements put in place by last year's omnibus banking act, new initiatives are being prepared on the legislative front that could renew the shock waves. The first is a tax-cut bill with an expected provision increasing incentives for savings. Variations on this theme -- which would be a windfall for hard-hit thrifts -- include tax incentives to promote home ownership for first-time buyers and to allow more persons to provide for their own retirement plan.

Two of the most controversial issues affecting banking are interstate branching and cross-industry acquisitions. The Carter administration recently endorsed a gradual relaxation of the prohibition against banks in one state accepting deposits from another. Last fall the Senate tried to put a moratorium on the acquisition of savings and loans by bank holding companies; the House declined to go along. Both topics can expect extensive airings this year, but action probably won't come for some time.

Commercial banks face decreased profits in 1981, according to Richard Stillinger, vice president of Keefe, Bruyette and Woods. The firm's analysis of 24 regional and money center banks indicates that earnings on average will be up 8 percent in 1981, compared with 10 percent in 1980 and 16 percent in 1979. The primary reason for the anticipated difference is the performance of interest rates. When they plummeted in the second quarter of 1980 money center banks lowered their prime rates more slowly and consequently profited. With no sudden drop in interest rates foreseen this year, there will be no opportunity for wide spreads. Furthermore, there will be no big difference between big and small banks' profits as happened during the extraordinary situation last year.

Lawrence R. Fuller of Drexel, Burnham, Lambert is more optimistic. He looks for 10 percent growth, which as he points out, is negative real growth when inflation is factored in. Money center banks can anticipate a return on equity of 14 percent to 15 percent in 1981. Fuller's optimism is based on a continuing demand for credit and a dampening of the volatility of interest rates.

"For 1980 as a whole, it is expected that savings and loans will earn no more than 13 cents on every $100, the lowest return on assets since the 1930s. Moreover, however, is an increasing probability that 1981 earnings will be even worse than 1980, which would place them near zero." This dire prediction comes from Dale P. Riordan, who was until recently with the Federal Home Loan Bank Board and who is now chief economist of the National Savings and Loan League.

The only way this fate can be avoided is for interest rates to fall quickly this year. Should this unlikely event occur, says Riordan, 1981 return on assets could reach 20 cents. By way of comparison, the previous low in this era was 43 cents in the first half of recession-plagued 1975. In the "good old days" of 1978, it was 83 cents.

There seems to be general agreement among forecasters that savings and loans are doomed to experience negative earnings during the first half of this year, followed by a slight improvement during the last six months. Innovations like NOW accounts and flexible-rate mortgages will not be developed enough this year to affect the earnings of the vast majority of thrifts. Jonathan Gray, who follows stock S&Ls for Sanford C. Bernstein & Co., predicts that 1980 earnings will be off 80 percent to 90 percent from the previous year. As for the first quarter of 1981, "it will be alarmingly similiar to the second quarter of 1980. Unless interest rates plummet during the first quarter, S&Ls will face having to roll over at 14 percent $88 billion in certificates of deposit that were purchased at 8 percent to 9 percent six months earlier.

Richard Marcis, chief economist of the Federal Home Loan Bank, is slightly more optimistic, predicting a return on assets of 40 cents per $100 during the second half. His outlook for mortgage lending is $80 billion, compared with $71 billion in 1980 and $100 billion in 1979 Riordan's description of mortgage activity this year is "in a word, terrible." Mortgage interest rates, he projects, will be in the 14-to-14 1/2 percent range during the first quarter at best. For the year as a whole, they will not fall below this summer's low of 12 1/2 percent. Mortgage funds will continue in short supply so long as institutions find it more profitable to pour the funds into short-term investments or stay liquid in periods of volatile interest rates rather than make long-term loans to homeowners.

The situation is even worse for mutual savings banks, according to George Hanc, chief economist of the National Association of Mutual Savings Banks. Deposit outflows, which reached $4.5 billion last year, will be about $3 billion in 1981, the industry's fourth consecutive year of disintermediation. At the time of his predictions in mid December, seven out of 10 New York mutuals were operating in the red.Hanc gave them the bad news: a net loss of 15 cents on $100 in 1980, followed by a loss of 25 cents this year. One saving grace, the savings banks' surplus position is still comparable to those of savings and loans and many commerical banks.

Due to increased competition and the need for more efficient operations, plus a continued unfavorable economy, substantial contractions are predicted for the banking industry. There are today some 42,000 depository institutions in the country, of which about half are credit unions, 15,000 are banks and the rest savings banks and savings and loans. (By way of comparison, Canada, Great Britian, France and West Germany combined have fewer than 700 commercial banks.) Riordan anticipates that the number of mergers between S&Ls will double in 1981 to 200. That is double again the 45 mergers that occurred during the last good year, 1979.

Through the financial gloom shines a brighter world of technology. In 1981 look for more experiments involving home computers like those pioneered last year by Banc One of Columbus, Ohio. This allows a customer to see bills displayed on his or her television screen and to push buttons to order them paid.