President Carter's campaign committee and the National Bank of Georgia have agreed to pay $6.200 in penalties for illegal political use of the bank's private airplane in 1975-76, the Federal Election Commission announced yesterday.

The civil penalties were agreed to by all parties after Carter committee and the NBG had initially pleaded that the campaign's failure to reimburse the bank for five flights was a bookkeeping oversight and not a willful violation of law.

Yesterday's settlement deals with the least controversial problem outstanding between the president's campaign organization and the FEC. Audits of the Carter primary and general-election campaign operations are still incomplete: both deal with questioned expenditures of funds far larger than the money involved in the bank-financed plane flights.

The issue arose last summer during investigations into the affairs of Bert Lance, who subsequently resigned as Carter's budget director and earlier had headed the Atlanta bank. Lance acknowledged that as bank president he had often made the aircraft available to favored customers. Carter among them, and that some flights were made after the former Georgia governor had begun his presidential quest.

Carter aides later acknowledged that the five short flights, four in 1975 with Carter aboard and a fifth in September 1976, were at least partially connected with the campaign and should have been paid for. It is unlawful for a corporation to make service or equipment available to a political candidate without reimbursement.

The Carter campaign committee sent the bank a check for more than $1.100 last August to cover the cost. The bank refunded about $300 after recalculating the expenses.

Lance testified that he had once contacted a campaign staffer about reimbursing the bank, but the issue somehow was forgotten. Presidential press secretary Jody Powell and others also have said the matter was an oversight.

When FEC took up the case last year, the bank argued that Lance was the only officer who knew of the flights and hence the firm should not now be punished for contributions of which it was not aware.

The "conciliation agreement" reached with the FEC, formally announced yesterday, stipulates that neither side admits any deliberate wrong-doing. However, the FEC said "the failure of the (Carter) committee to pay for the use of the . . . aircraft until August 1977 constituted its receipt of in-kind contributions, in violation" of the Federal Election Campaign Act.

Similarly, the FEC document said the bank's failure to bill the committee until that date constituted an unlawful contribution.

An attorney for Carter's committee said the $1.200 fine would be paid out of contingency reserves for post-election purposes. The bank will pay $5,000.