Continental Illinois National Bank, the seventh largest in the country, yesterday announced a quarter-percent increase in the prime interest rate to 8 1/2 percent.

"We decided that, with our strong loan demand and the way the cost of funds has moved up, our prime ought to be higher, so we moved it," explained Continental Illinois Chairman Roger Anderson.

Anderson cited recent Federal Reserve actions to increase the key federal funds rate. "The whole cost structure has followed this," he said.

The Fed said in this weekly money supply report yesterday that the federal funds rate (which it uses as a bench mark for money market operations) averaged 7.43 percent for the week ended May 24, up from 7.34 percent in the previous week.

The money supply dropped $100 million in the latest statement week after a sharp $4.3 billion decrease the week before.

The Continental Illinois chairman predicted that the boost in the base lending rate for high-grade corporate customers that his bank initiated - effective today - will spread quickly through the banking industry.

And he forecast a prime rate of 8 3/4 to 9 percent by the end of 1978.

Citibank, which calculates the prime rate on a formula of 1 1/4 percent above the three-week moving average for 90-day commercial paper, is expected to raise its prime rate to 8 1/2 percent this morning.

Some interest rate analysts are forecasting a prime rate of 9 1/4 percent or higher by the end of this year, raising concern about a credit crunch that could send the U.S. economy into a recession by mid-1979.

The last increase in the prime rate was initiated by Chase Manhattan Bank on April 28 when it raised the rate to 8 1/4 percent.

Anderson said his bank's loan demand was up almost 16 percent in the first quarter over the same period in 1977, and since then has climbed even more briskly.

"A strong domestic loan demand was a long time coming in this recovery, but it finally came," he noted. "We saw it beginning to get strong at the end of the last quarter of 1977, and it's continued to be strong. We keep looking to see if we can discern any geographical or industry concentration, but it seems to be across the board.

But, responding to some recently voiced concern that the banking system is getting strapped for liquidity, Anderson said "the banks are in relatively good shape to absorb additional loan demand."