Last week's action by the Federal Reserve Board to ease credit conditions means mortgage interest rates will be coming down. The questions are: how fast and how far?

The Fed's "detour" from using the growth of one measure of the money supply -- M1, the total of currency in circulation and checkable deposits -- as a guide to policy, and a cut in the Fed's discount rate from 10 to 9 1/2 percent, helped push down most interest rates.

As usual, mortgage rates were more slow to change. But the decline in other rates, which with a lag will cut the cost to thrift institutions and other mortgage lenders of obtaining lendable funds, means mortgage rates, too, will be coming down.

In the wake of the Fed move, the federal government itself aggressively sought to lead the way by cutting from 13 1/2 to 12 1/2 percent the allowable rate on single-family home loans insured by the Federal Housing Administration or guaranteed by the Veterans Administration. The rate was dropped from 14 to 13 1/2 percent less than three weeks ago.

Citibank in New York lowered its 30-year variable-rate mortgage (on which the interest rate is adjusted every six months in line with changes in the six-month Treasury bill rate) to 12 1/4 percent this week. Three months ago the bank was charging 15 1/2 percent for such loans.

In California, the Crocker National Bank dropped its rates on fixed-payment 30-year loans from 15 1/2 percent to 14 1/2 percent. The Bank of America similarly reduced the rate is charges on adjustable-rate mortgages from 16 percent to 14 1/2 percent on loans below $150,000, and from 16 1/2 percent to 15 1/2 percent for loans larger than that.

Some California S&Ls, which already had pushed their variable-rate loan charges down to 14 percent or less, knocked off another percentage point. However, some institutions were charging a significant number of "points" as an upfront cost to get these loans. A point equals 1 percent of the original value of the loan.

Marine Midland Bank in New York lowered its rates on adjustable-rate mortgages from 15 percent to 14 percent, and Manufacturers Hanover Trust Co. also knocked a percentage point off its rates.

Mortgage rates at many institutions have been slower to fall, however, and a number of analysts expect them to continue to decline only gradually.

The Federal Home Loan Bank Board reported that at savings and loan associations the new commitment rate on 25-year, 75 percent loans fell about three-fourths of a percentage point from early August to early September, when it reached 16.23 percent.

Separately and more recently, the Federal Home Loan Mortgage Corp. said a sample of savings and loan associations reported their commitment rate on new loans with a 20 percent down payment was down to 15.1 percent in the first week of October. That was the lowest rate in nearly two years for that group of S&Ls.

Economist M. Kathryn Eickhoff of Townsend-Greenspan & Co., an economic consulting and forecasting firm, said the recent sharp declines in most interest rates means that "mortgage rates will be coming down more than we had hoped. We think we will get a marked decline, but not as rapidly as in other rates."

The Townsend-Greenspan forecast calls for conventional mortgage rates at closing, which includes amortization of certain other costs associated with a loan, to average about 13 1/2 percent next year, falling to around 13 percent late in 1983.

Maurice Mann, an economist who formerly headed the San Francisco Federal Home Loan Bank and is now with Warburg Paribas Becker, Inc., expects mortgage rates to fall to around 13 percent by the end of this year, not next year.

Only last month, the economic advisory board of the National Savings and Loan League, which Mann chairs, said mortgage rates were likely to be about 14 1/2 percent late this year and about 13 1/2 percent late next year. "We have had a couple of major events since then," Mann said. "Things have moved a lot faster than I expected, and I would have to shade those numbers downward."

If mortgage rates do come down the roughly 3 percentage points predicted by Eickhoff over the next year, it is unclear how much of a spark that will provide for the housing industry or the resale housing market. Clearly it will help these recession-battered sectors of the economy. Again, the question is how much. The faster move seen by Mann should generate much more housing sales and construction activity.

Allen Sinai of Data Resources, Inc., another economic forecasting firm, is cautiously optimistic, but no more than that.

"The crisis in mortgage finance is easing, with interest rates lower, some evidence of better deposit inflows at thrift institutions beginning to appear, and mortgage rates down 2 or 3 percentage points since midyear," Sinai said. "The low housing starts performance of August will likely be the trough, and homes sales activity should begin to rise now."

On the other hand, Sinai cautions that the problems of the thrifts are far from over. "The net worth of thrifts will still decline for much of the rest of this year and the shakeout of thrift institutions still has another six months to go, with mergers and absorptions of thrifts to continue," he warned.

Specifically, Sinai said the effective conventional commitment rate for mortgages should average about 15.3 percent this quarter, down about 2 percentage points from the second quarter average.

Despite the swift decline in money market interest rates, the cost of lendable funds to the S&Ls will decline only very slowly. The average for the second quarter was 11.63 percent, and DRI thinks it will drop only to 11.14 percent on average for this quarter.

The principal reason for the slow change in the institutions' cost of funds is the nature of their deposits.

In August, 16.6 percent of the funds in federally insured S&Ls were in regular passbook accounts and another 2.1 percent were in transaction accounts. Both types of accounts pay such low rates now that they are not apt to fall.

Another 23.9 percent of deposits are in 2 1/2-year certificates, which mature slowly so that rate declines take a long time to be reflected. Also, those coming due now were issued in 1980 when the rates were not as high as they have been more recently.

The S&Ls also have 10 percent of their deposits in large certificates of deposits, $100,000 or more, which are issued with varying maturities. Another 33.1 percent is in six-month money market certificates, which roll over fairly quickly.

In the short run, the biggest impact on the thrifts' cost of funds may be a quick decline in the interest rates they have to pay on the $66 billion in advances they have from the Federal Home Loan Banks. The San Francisco FHLB last week, for instance, cut the rate on its advances to 9 percent.

With many thrift institutions still losing money, they are going to be reluctant to cut mortgage rates on new loans as rapidly as they might in better times. Normally, an 11.14 percent average cost of funds would translate into mortgage rates in the range of 13 to 13 1/2 percent. The many older loans with much lower rates still on their books is a major spur to try to return to profitability by keeping the spread between the cost of funds and new loan rates larger than normal -- if competitive pressures allow.

Mann thinks such pressures will force mortgage rates downward more quickly than is really in the institutions' interest. "They are going to be under tremendous competitive pressure," he said. "I don't think they will be able to resist it even if they should."

Even if mortgage rates do come down, there is great uncertainty about exactly how that will translate into housing sales and construction. DRI's Sinai noted that "affordability remains as a major demand-side constraint even with the significant declines in mortgage rates." And Townsend-Greenspan's Eickhoff said that monthly mortgage costs on a median priced new home still are about $900, a figure beyond the means of many buyers.

In the short run, the analysts expect increased mortgage availability and the drop in rates to be used to a significant degree to refinance existing "creative financing" packages that are coming due in the form of massive balloon payments. In the Washington area, some mortgage companies that have participated in such financing packages are reported to be getting calls from buyers who want to refinance and reduce their payments, even if they are not facing immediate balloon payments.

Aside from refinancing, some of the increased ability of institutions to provide funds at a more reasonable level of rates will simply displace the financing sellers have been forced to provide over the last two years or so if they wanted to make a sale.

Finally, with the resurgence of the stock and bond markets, some of the money that has been provided by investors buying mortgage-backed securities may be diverted to other investments. In the first half of this year, such investors put $20.4 billion in mortgage-backed securities guaranteed by the Govenment National Mortgage Association, the Federal National Mortgage Association of the FHLMC. That was close to the record annual volume of $25.1 billion set in 1979.

These cross-currents probably add up to a still slow recovery for housing. Eickhoff, for example, expects housing starts to rise only to about a 1.4 million unit annual rate late next year, up from about a 1.2 million rate this quarter.