Consumers increased their outstanding installment credit by $2.45 billion in August, almost the same rate as in July which was the smallest increase since the beginning of 1978, the Federal Reserve Board said yesterday.

In June, consumer credit expanded by $2.56 billion and in May by $3.73 billion.

The total outstanding as of August was $299.8 billion, up 15.5 percent above a year ago.

Consumers were borrowing and repaying loans in August at a rate that would expand outstanding credit 10 percent a year. That compares with a 15-percent rate of expansion in the first half of 1979 and a 19-percent in 1978.

An economist at the Fed said the August figures are "consistent with the general pace of the economy. Consumer spending has slowed. Disposable personal income growth has slowed."

New borrowing using credit cards, automobile and mobile home loans, and personal loans totaled $27.6 billion, the largest monthly amount except for last May's record of $27.9 billion.

However, consumer also paid off a record $25.1 billion worth of debt in August.

Indebtedness related to credit cards went up $787 million in August, up more than 8 percent from the previous month. Mobile home debt rose by $182 million.

Debt related to auto purchases rose by $594 million, about 4 percent less than in July, the Federal Reserve said.

Last month Comptroller of the Currency John Heimann asked the 4,600 national banks he regulates to be more careful in extending credit to avoid any possible "excesses."