A headline in Tuesday's Business section incorrectly referred to Penn Central Corp. as a railroad firm. It is engaged in energy, electronics and telecommunications, and real estate activities.

Continental Illinois Corp., which was saved from failing by a massive government rescue last summer, yesterday displayed the benefits both of the bailout and of declining interest rates.

The giant Chicago bank company reported a fourth-quarter profit of $36.6 million (12 cents a share), 49 percent higher than the $24.5 million (57 cents) it earned in the final three months of 1983.

As a result of the bailout, there are the equivalent of 200 million Continental shares outstanding today, compared with 40 million in the last three months of 1983.

Most of the nation's biggest bank companies benefited, like Continental, from declining rates in the open market, where these banks raise a large portion of their funds.

The impact of the declining rates outweighed the continuing drag on bank earnings that comes from a high level of problem loans, including loans to Third World countries.

BankAmerica Corp, for example, yesterday reported fourth-quarter profits of $73 million (35 cents), up from $53 million (22 cents) in the final three months of 1983.

BankAmerica owns the Bank of America, the biggest bank in the United States. The bank company attributed the 39 percent increase in its fourth-quarter profits to sustained growth in net interest revenue (the difference between what a bank pays for its funds and what it earns on its assets) and fee income.

Like most other banks, BankAmerica turned in a 1984 performance that was far less stunning than its fourth-quarter results. For the year as a whole, BankAmerica had profits of $375 million ($1.96), down 4 percent from the $390 million ($2.18) it earned in 1983.

Continental for the year reported the biggest loss in banking history -- $1.1 billion -- all the result of the federal bailout that permitted Continental to remove $3 billion of bad loans from its books.

Under the terms of the rescue, the Federal Deposit Insurance Corp. paid $2 billion for those loans. Continental shareholders took a $1 billion loss on the transaction. That capital was replaced by the FDIC, which received preferred stock that can be converted into 160 million shares of Continental common stock.

The FDIC also said it would buy up to another $1.5 billion in bad loans from Continental at their face value as of last May.

Continental Chairman John E. Swearingen, who was brought in by the FDIC to run the parent company, said that the earnings increase occurred both because the rescue relieved it of a large number of low-yielding problem assets and because net interest income rose by more than 40 percent over the third quarter. The increase in net interest income reflected both declining rates that all bank companies enjoyed, and a lessening in the premium over market rates that Continental must pay.

Continental still needs the umbrella of the federal government and a consortium of other big banks to raise enough funds to keep afloat. A massive run on Continental deposits last May triggered first an emergency rescue, then the permanent bailout. But the bank company reduced its borrowings from the Federal Reserve to about $2.9 billion on Dec. 31, compared with an average of $6.1 billion in the third quarter. It has had an average of $4.1 billion outstanding on its bank credit line for about six months.

Continental's spread between borrowing costs and lending rates averaged 3.10 percentage points in the fourth quarter, compared with 2.11 points for the year as a whole and 2.53 points in 1983. BankAmerica's net interest margin was 4.18 percentage points, up from 3.71 points from the final three months of 1983.