Security Pacific Corp.'s acquisition of American Finance System Inc., a large consumer finance company based in Silver Spring, was approved yesterday by the Federal Reserve Board.

Based in Los Angles, Security is the nation's 11th largest commercial banking company and holding company for Security Pacific National Bank, the second-largest California bank.

Security's takeover of American Finance will give the West Coast firm a large base of small loan offices throughout states east of the Mississippi, in competition with industry leader Household Finance Corp., and other independents and consumer finance subsidiaries of banking firms.

In a separate development, the Silver Spring firm said president Bruce Cunningham will become chief executive on Jan. 1, succeeding M. L. Goeglein, who has relinquished the chief executive's post but will continue as board chairman. Goeglein has been credited with turning around AFS operations in the past two years.

Last year, AFS earnings rebounded sharply to $6.2 million ($1.17 a share) compared with $2.8 million (46 cents) in 1976. Founded here in 1930, the company suffered badly during the recession of the early 1970s, as interest rates soared -- making money to lend more costly. Some small loan offices were closed and dividend payments were halted.

Several earlier proposed mergers since 1969 with other finance companies or bank holding companies, either were dropped by mutual agreement or blocked by the Federal Reserve Board, which must approve acquisitions in bank-related fields by bank holding companies.

Under terms of the AFS-Security Pacific agreement, all common and preferred stock of AFS will be acquired, and the Silver Spring firm will be merged into Amfisco Inc., a Security subsidiary.

Each share of AFS common will be exchanged for $10 in market value of Security common; each share of AFS 6 percent cumulative preferred will be exchanged for $25.25 cash plus unpaid dividends ($4.87 as of Sept. 15); and each share of AFS $6.75 cumulative preferred will be exchanged for $103.75 plus unpaid dividends ($21.94 as of Sept. 15).

A favorable tax ruling has been obtained from the Internal Revenue Service, meaning that no gain or loss will be recognized by holders of AFS common.

Company officers said yesterday they plan to move swiftly to consummate the merger by next Friday. It was first proposed last year.

A major attraction of the Silver Spring company is the AFS string of 370 small loan offices in 22 states, many of which ring the Washington district limits. In the new era of electronic money transactions that transcend traditional barriers to doing bank business across state lines, large U.S. banking businesses are moving rapidly to establish nation-wide consumer loan operations. One day, these offices may be transformed into facilities that offer a wider range of financial services.

AFS earnings in the first six months of 1978 were depressed by higher interest rates, as net income fell to $2.4 million (41 cents a share) from $4.1 million (59 cents) in the 1977 period, which had included an extraordinary gain.

In addition, AFS suffered legal expenses in fighting a competing tender offer from Aristar, of Miami, which was withdrawn earlier this year.