Short-term interest rates have tumbled in the last month, but long-term rates, including mortgage rates, are likely to take a lot longer to come down from their lofty perches, analysts say.

Unless short-term rates should suddenly reverse themselves, the rate on 30-year fixed-rate mortgages probably will be close to 15 or 15 1/2 percent by the end of the year rather than today's 16 1/2 percent level, according to Timothy Howard, chief economist for the Federal National Mortgage Association (Fannie Mae).

That would be a far more gentle decline in mortgage rates than the one that is occurring in the short-term market.

Until the last few years, mortgage rates mainly were dependent on the perceptions of managers of savings and loan associations and mutual savings banks who took in cheap deposits and loaned them out to home buyers.

Today, however, deposits are no longer cheap. Passbook savings accounts paying 5 1/2 percent are shrinking, and the funds are being tranferred to either money market certificates or money market funds. Savings and loans are unlikely to see a rush of money into cheap accounts again.

Since they already are reeling from their losses of recent years, savings institutions will be reluctant to lower sharply the rate they charge for mortgages, no matter what happens to their cost of funds. They have huge losses to make up for.

The highly publicized prime rate has fallen 1 1/2 percentage points in the last three weeks, and many economists expect it to fall another half percentage point to 14 1/2 percent as soon as next week. Other short-term rates, those set in the so-called money markets where banks and businesses buy and sell funds, have declined even more dramatically.

In late June, big banks had to pay about 15 percent to raise funds for three months (by issuing jumbo, $1 million certificates of deposit). Now they are paying about 11 1/2 percent or less--one of the reasons bankers are cutting the rates they charge businesses.

Short-term rates have fallen for two major reasons: the Federal Reserve Board has loosened up its tight monetary policy, and business demand for short-term credit has started to ebb, although by historical standards it remains extremely high for the late stages of a severe recession. Whether short-term rates will continue to fall is a matter of serious debate among economists.

As a result, individuals and institutions that lend money remain cautious about committing their funds for a long time: whether it be for a 30-year mortgage or a 25-year corporate bond.

"For a long-term lender, it's not short-term Federal Reserve policies but the long-term outlook for inflation" that is critical, according to Edward Boss, the financial economist for Continental Illinois National Bank and Trust Co.

Long-term lenders have been hit hard during the last four years of double-digit inflation and sky-high interest rates. Savings and loan associations have been losing money apace, and the rate of failures among these mortgage specialists is running at a record rate.

Similarly, bond owners have watched the value of their once-stable assets tumble as interest rates skyrocketed.

As a result, investors have been more likely to put their funds in short-term investments--from Treasury bills to money market funds to six-month, market-rate certificates at their local bank or savings and loan. It will take some time, nearly all economists say, before many investors are willing to put their funds into longer-run, riskier investments.

With the government borrowing at a record pace to finance the burgeoning federal deficits and doomsayers warning that the recent decline in interest rates will not last, many investors who otherwise might be tempted to "lock-in" a 15 percent return on a corporate bond are keeping their money parked in short-term investments--such as money funds or Treasury bills--whose yields have been declining in recent weeks.

Nevertheless, for the first time in about a year, short-term interest rates are substantially below long-term rates. "When investors realize that short rates are not a one-month phenomenon, I think what we'll find is that they begin to reach out investing longer-term to pick up yield," said Howard of the Fannie Mae.

If that occurs, and more and more funds are willing to take the long-term plunge, rates should fall out of simple supply and demand. Yet, because companies have been nearly as unwilling to sell long-term debt as investors have been resistant to buying it, declines in long-term rates probably will trigger a groundswell of corporate bond offerings. Already, many companies have been rushing to sell five-year and 10-year bonds because of moderate declines in interest rates in the so-called intermediate market. As a result, even if investors are willing to put out their funds for a longer period, the increased numbers of borrowers seeking those funds will help keep rates up.

That will make it harder for mortgage rates to fall. For as savings and loan associations lose depositors--not just those with passbook accounts but even those who put their money in higher-cost accounts--the thrift industry is becoming a less important source of mortgage money. Instead, more and more home loans are being made, in effect, by the same market that buys corporate bonds. According to Howard, about half the mortgage loans made today are packaged into so-called pass-through certificates that are then sold to investors in the open market.

The home mortgage loan of the past was a loan unto itself--made by institutions specifically designed to aid the housing market whose costs were protected by federal interest ceilings. Now the standard home mortgage loan competes with corporate bonds and Treasury securities more than it ever did in the past.

"When you look at the current rally in interest rates, you'll see that the rally in bonds has been more hesitant and backed up than the rally in short-term rates, according to Continental's Boss.

When the bond market stages a true rally, rather than the evanescent sort typical of the last three years, mortgage rates will decline substantially. Experts have been hoping for, and sometimes (wrongly) predicting such a rally for the better part of those three years.