BOSTON -- The interest rate on 30-year fixed-rate mortgages is expected to rise to at least 12 1/2 percent by June, causing a significant drop in the construction of homes and in the number of new loans, key housing and banking officials said this week.

At the same time, the higher rates on fixed mortgages are expected to spur a continued increase in the use of adjustable-rate mortgages, which may rise above 9 percent next year.

Next year "is not going to be a particularly good year for mortgage bankers or first-time home buyers," Lyle E. Gramley, chief economist for the Mortgage Bankers Association of America, said at the trade group's 74th annual convention here this week.

Since March, when interest rates dipped below 9 percent in many parts of the country, the rates on 30-year fixed-rate mortgages have jumped 2 1/4 percentage points. Rates on the 30-year fixed-rate loans rose to 10.88 percent early this month, and rates on one-year adjustable-rate mortgages rose from 7.74 percent in May to 8.15 percent in early October, the MBA said.

Adjustable-rate mortgages have attracted large numbers of home buyers who do not want to get locked into the higher fixed rates. An MBA telephone survey of 23 firms from throughout the country, released at the convention found that 39.7 percent of their business in September was in adjustable-rate loans, up from 18.5 percent in May.

Convertible adjustable-rate mortgages -- which allow borrowers to switch from a varying interest rate to a fixed rate, usually within the first five years of the mortgage -- accounted for 26 percent of the total ARM volume, the MBA said.

But some mortgage bankers said that some of the adjustable-rate mortgages are not economically sound.

"ARMs are the hot topic, no ifs, ands or buts," said Willard A. Gourley Jr., chairman of Barclays American Mortgage Corp. in Charlotte, N.C. "But some of these rates really aren't practical. You're going to see some of those low rates disappear over the next week after many {lenders} realize the high cost of money."

Within the past three months, lenders have felt that higher cost through the tightening of the Federal Reserve's monetary policy. The discount rate and rates on three-month Treasury bills, which lenders use as guidelines to set their mortgage rates, have been steadily rising during the past six months. The rise in the discount rate from 6 1/4 to 7 1/4 percent earlier this year has been one of the key reasons many lenders have raised the interest rates on mortgages. (The discount is the rate the Fed charges member banks for loans.)

As a result of the overall higher interest rates, the number of mortgage loans made since April has been cut nearly in half compared with last year. The number of refinancing applications, which had hit record levels last year, has dropped drastically.

According to the MBA survey, the number of refinancing applications fell to just 12 percent of residential lending in September, down from 34.5 percent in March and 42.4 percent in September 1986.

John M. Teutsch Jr., the MBA's incoming president, said the higher interest rates are causing home buyers to be much more picky about the kinds of mortgages they get.

"Higher interest rates erode the home buying affordability of many families, and they understandably look for ways to maximize their financial resources," said Teutsch, who is president and chairman of the executive committee of CompuFund/Network Funding Corp. in Seattle.

Higher rates have taken a toll around the country. Many of the Sun Belt states, such as Texas and Oklahoma, are hardest hit, particularly since their economies have not yet recovered from depressed oil prices.

Ronnie J. Wynn, president of Colonial Mortgage Co. in Montgomery, Ala., said single-family home sales in such Texas cities as Dallas and Austin are down nearly 40 percent. The delinquency rate on single-family loans totals more than 7 percent in Texas and Oklahoma.

"Many areas are showing a great deal of weakness," Wynn said. "And as rates increase, it will cause greater weakness."

The Northeast and parts of the West are still the strongest real estate markets, but they are not without their problems.

Robert J. Spiller, chairman and chief executive officer of the Boston Five Cent Savings Bank, said that sales of condominiums are very slow, that home prices are continuing to rise, and that is is taking between 60 and 90 days longer than the normal 30 days to sell a home once it has been put on the market.

The median price of a single-family home in the Boston area, which was about $137,100 in June, is now about $175,800, he said. "House prices are too high and need to be lower," Spiller said. "They're taking a lot of people out of the market."

Teutsch said a resurgence in the timber and agriculture industries has helped keep home sales stable in California, Washington and Oregon.

But Alaska and Colorado, both with heavily oil-based economies, are struggling. Alaska, for instance, has an 11.23 percent delinquency rate on its single-family loans compared with a 4.4 percent average rate in the West as a whole, Teutsch said.

MBA's Gramley said parts of the Midwest will continue to have a hard time, while many cities in the South will keep the momentum of the past several years. However, he said the total number of U.S. housing starts will drop about 10 percent this year to about 1.45 million, the lowest number since 1982.