Inflation continued at a moderate pace in June as producer prices for finished goods rose a seasonally adjusted 0.6 percent, or about a 7 percent annual rate, the Labor Department reported yesterday.

The increase was larger than May's 0.4 percent rise but still well below most monthly increases over the last two years. Finished goods prices rose 10.2 percent in the most recent 12 months.

Meanwhile, the Federal Reserve Board said consumer installment credit outstanding rose $1.35 billion in May, less than the $2.33 billion increase in April, due to smaller growth in revolving credit and a decline in automobile credit.

The continued better news on the inflation front is apt to continue, according to most forecasters. The sharp drop in the inflation rate is primarily a result of the unexpected softness in world oil prices and the equally surprising stability of food prices. And lately there is some evidence that wage increases have become somewhat smaller.

Economist Ott Eckstein of Data Resources Inc. said the first two developments alone have lowered his forecast for finished goods prices by 4 1/2 percentage points for the year ending next March. For all of 1981, Eckstein expects finished goods prices to be up 9 1/2 percent and for next year up only 8.3 percent. They climbed 13 1/2 percent in 1980.

Part of this improvement is a result of a flat economy, and part of it, such as the virtual absence of food price inflation, likely will not continue. But Eckstein and many other analysts think the change will last. "Experience teaches that inflation forecasting is a high-risk undertaking, but the current situation is safer than it has been in quite a few year," he said. "The fundamentals are pretty well in place, and it would take extreme events to upset them."

Lawrence Chimerine, head of the private forecasting firm Chase Econometrics of Bala Cynwyd, Pa., saw last month's increase as a low point between what happened in the past and what lies ahead. He said the June figure is "tremendously better than what we had a year ago and also a little less than what we're going to see in the months ahead."

Among finished goods, the June increases were about equally divided between consumer foods, which rose one-half percent, and other goods, which were up 0.6 percent.

The index for consumer food prices had showed no change in April or May.Beef and veal prices jumped 2.4 percent, while the price of pork, eggs, rice and sugar, all of which had dropped in May, rose in June.

Home heating oil prices rose 0.4 percent after a 1.2 percent decline the previous month. Gasoline prices fell 1.2 percent, but that was not as large as the 1.8 percent drop in May.

The intermediate goods index rose only 0.3 percent, the smallest increase in more than a year, the department said. Foods and feeds prices in this category declined one-half percent, the fifth such drop in the last seven months. Intermediate energy goods -- mostly oil products sold to industry --fell 0.7 percent, the largest decline since 1978.

The crude materials prices rose 1.2 percent largely as a result of a 2.8 percent increase in prices for foodstuffs and feedstuffs.

The Federal Reserve said that new extensions of consumer credit in May totaled $28.1 billion, down more than $700 million from the record level in April.

While $7.3 billion worth of auto loans were made, repayment of earlier loans was even greater, reducing the amount outstanding by $195 million, the Fed said. The amount of outstanding revolving credit cards, rose by $350 million in May, substantially less that the $838 million increase in April. Credit for mobil-home purchases outstanding increased $243 million while that for all other types of installment credit, mostly loans at banks and finance companies, rose $948 million, slightly more than in April.