While mortgage interest rates are hovering in the 8.75 percent to 9.5 percent range, many people with home equity lines of credit will be paying double-digit interest soon.

In the last round of credit tightening, the Federal Reserve pushed the rates it controls up by three-quarters of a percentage point, and banks raised their prime rates to match - up from 7.75 percent to 8.5 percent.Since most home equity lines are tied directly to the prime, that means a substantial increase in payments for many households. Rates on home equity lines generally are set about 1.5 percentage points above prime.

By next month, the average interest rate paid on home equity lines will reach 10 percent, said Keith Gumbinger of HSH Associates, a mortgage information firm in New Jersey. The current average, he said, is about 9.5 percent because not all banks rushed to raise the prime immediately after the Fed's last round of increases.

But banks are still offering low-ball introductory rates to attract customers, according to Robert Heady, publisher of the Bank Rate Monitor in Florida.

He said such gimmicks have left the average rate in highly competitive New York at 7.4 percent, compared with an average of 9.88 percent in Detroit - the highest rate in the top 10 markets.

The rise in home equity costs over the last year will wipe out some of the savings many households achieved by refinancing their mortgages in 1992 and 1993 when rates were low.

These payments are likely to be even higher next year if the economy remains as strong as it is now. Already, Federal Reserve Chairman Alan Greenspan has signaled that rates probably will rise again in coming months to hold down perceived inflation.

"There is no doubt whatsoever," Heady said. "Rates on home equity loans and lines of credit are going up, probably through 1995 and maybe through 1996."

If banks in your area are offering low introductory rates lasting six months or longer on home equity loans, take a look. You can save a lot of money during the introductory period as long as closing costs are minimal and the longer-term rate isn't higher than the average in your community.

Despite the rise in rates, Heady noted that home equity is "still one of the cheapest ways to borrow a sizable amount of money."

Right now, he said, the average interest rate nationally on credit cards is 17.9 percent, for unsecured personal loans 15.8 percent and for a car loan 9.39 percent.

Here is a sample of home equity lines, compiled by HSH Associates, currently being offered in various cities:

- Framingham Savings Bank, Boston: 5.99 percent, good until July 31, 1995, then prime plus 1.5 percent. (1-508-620-0300.)

- Atlantic Bank, New York: 6.5 percent for one year, then prime plus 1.25. (1-718-204-2613.)

- Citibank, Miami: 6.99 percent for one year, then prime plus 1.45. (1-800-374-9800.)

- Citibank, San Francisco: 4.75 percent for six months, then prime plus 1.25 percent. (1-415-781-3180.)

- Bank One, Denver: 6.99 percent for six months, then prime plus 1.5 percent. (1-303-455-2000.)

- First National, St. Louis: 9.5 percent, prime plus 1 percent. (1-314-862-8300.)

- Bank of America, Phoenix: 5.79 percent for six months, then one month CD plus 3.75 percent. (1-602-594-2371.)

- Liberty National Bank, Los Angeles: 8.5 percent untl July 31, 1995, then prime plus 1 percent. (1-714-895-2929.)

How payments rise

Loan 7.5% 10%

Amount interest interest

$30,000 $187 250

$50,000 $312 $416

$97,000 $606 $808