Mortgage interest rates continued to climb to record levels in December, topping 10 percent for loans on both new and older homes, the Federal Home Loan Bank Board reported yesterday.

The effective interest rate on new homes averaged 10.02 percent nationally, while on previously ocupied homes the rate averaged 10.06. In November the new home rate averaged 9.87 percent and the used home rate aveaged 9.97 percent.

In the Washington area, the bank board said, effective interest rates on new home mortgage loans fell slightly from 10.03 percent in November to 10 percent in December.

On previously occupied homes, the effective rate in the Washington area rose to 10.1 percent from 10.05 percent.

A year ago, new home buyers pai an average interest rate of 8.92 percent in Washington, while purchasers of older homes paid 9.12 percent.

The national average for new homes was 9.09 percent in December 1977; for previously occupied homes it was 9.12 percent.

As the same time that interest rates were soaring, in large part because of infiation and efforts by the Federal Reserve Board to restrain the growth of the money supply home prices were climbing.

A new home in Washington a year ago cost an average of $67,200, the bank board said. Last month the average price of a new house was $87,500. Previously occupied houses cost an average of $88,000 last month, up from $77,900 in December 1977.

The average home buyer nationally paid $67,600 for a new house and $58,000 for an older home.

Builders expect that new home sales will decline next year, although high interest rates and rising purchase prices do not appear to have taken the wind out of housing sales.

With inflation continuing at a high rate, however, the Federal Reserve Board is expected to continue its tight money policy and perhaps become even more stringent. As a result, new deposits at savings and loan associations probably will slow.

This summer, as interest rates began to climb, savings and loan associations began to offer depositors special short-term, high-yield certificates of deposit whose interest rates were tied to yields on Treasury bills, the traditional haven for small investors during periods of soaring nterest rates.

But with Treasury bill rates now over 9 percent, S&Ls are finding ti increasingly expensive to sell the certificates and use the proceeds to make new mortgage loans.