Continental Illinois Corp. of Chicago reported yesterday that the Federal Deposit Insurance Corp. has lost about $28 million so far on $3 billion in problem and bad loans it purchased from the bank company last September in the largest federal rescue ever of a failing business.

Meanwhile, First Chicago Corp., parent of that city's other multinational bank, reported that the Securities and Exchange Commission is investigating all the bank company's loan charge-offs dating back to Jan. 1, 1982.

First Chicago shocked the investment community last month when it announced it would have to write off $278 million in bad loans. The bank company disclosed in a filing with the SEC that the agency was investigating the timing of loan charge-offs the bank has made in the last 33 months and whether improper insider trading of First Chicago stock occurred before the company announced its loan problems.

The costs the FDIC incurred carrying Continental's bad loans were about $39 million, while $11 million in interest was collected, Continental said in its own SEC filing.

The FDIC has hired Continental to collect loans that were once on the bank's books and also has agreed to buy up to another $1.5 billion in problem loans from the bank company within the next three years. The FDIC acted to clear bad loans from Continental's portfolio to permit the bank company to make a profit and restore depositor confidence.

The $28 million in FDIC losses were incurred between July 25 and Sept. 25.

Continental shareholders lost $1 billion on the loan sale to the FDIC -- which paid $2 billion for the package. The FDIC has a lien on the remaining $800 million shareholder investment in the bank company, the parent of Continental Illinois National Bank, to cover potential losses on the loans it bought. FDIC officials said it had expected the loss, which was why the agency demanded a lien on the remaining funds.

At the rate the FDIC is losing money on the loans it purchased -- roughly $168 million a year -- Continental shareholders will lose all of their stake in the big bank company within five years -- the time period in which the FDIC has a lien on the shareholders' stake.

Continental shareholders were also given the option to buy stock in the cleaned-up Continental at $4.50 a share until Nov. 26 and at $6 a share for the 22 months after that.

In its SEC filing, First Chicago -- which owns First National Bank of Chicago -- disclosed that it had reached an agreement with the Comptroller of the Currency to boost its ratio of capital to assets from the current level of about 5 percent to 6 percent.

Other big bank companies, including the giant BankAmerica Corp., have made similar pledges. Because of prodding from regulators and because of their own concerns about the increasingly volatile banking environment, bankers have been raising new capital and adding to their loan loss reserves.