Challenges, choices for home buyer.

The American dream of home ownership appears to be growing more elusive because of high mortgage rates. As a result, activity in the housing industry is slowing.

Despite this, industry experts have been surprised at how well sales have held up in the face of high mortgage rates.

''Home buyers stopped withholding demand once they became accustomed to somewhat higher interest rates,'' notes Beth Castiglia, an economist at the investment banking firm of Goldman, Sachs.

So although industry experts are predicting less robust activity, most are not forecasting a housing industry recession of the severity experienced in 1981 and '82. There will be ''a gradual weakening in activity'' between now and '86, argues Donald Straszheim, vice-president at Wharton Econometric Forecasting Associates.

''Housing peaked in March, and everything I know of - including (housing) starts, (building) permits, builders' plans, and (sales) traffic is down,'' says Michael Sumichrast, chief economist at the National Association of Home Builders. He expects 1.52 million housing starts next year, a level he terms ''a slowdown rather than a recession.'' In 1981 and '82, starts slowed to a 1.1 million annual rate.

A key reason for the expected slowdown is that homes are becoming less affordable. The National Association of Realtors (NAR) reported Tuesday that its housing affordability index fell in July for the third consecutive month and posted the largest monthly decline since November 1980.

In July, a family with the median national income of $25,583 had only 83.3 percent of the cash flow it needed to buy the median-priced existing home, which cost $74,700. Half of the nation's families earn more than the median income and half earn less; likewise half the homes cost more than the median and half cost less.

The index assumes a 20 percent down payment and also assumes lenders will not grant a mortgage if a family must spend more than 25 percent of its income on mortgage principal and interest payments.

Some economists quibble with certain technical aspects of the index, but they say the picture of declining home affordability it gives is accurate. And some forecasters say that with mortgage rates expected to rise slightly by year's end , the affordability picture could deteriorate further.

For instance, in 1970, roughly 60 percent of US households could afford the median-priced new home. This year, only 30 percent of US families can afford such a home, which in July cost $95,600. And next year, only 25 percent of US families may be able to afford a new house, notes Jesse Abraham, a housing expert at Data Resources Inc., a forecasting firm.

In his calculations, economist Abraham uses the interest rate available on a conventional loan with a 25 percent down payment. And he assumes a lender will reject a family that has to spend more than 25 percent of its income on mortgage payments.

While rising prices for existing homes have played a role in pushing house prices out of reach for many Americans, ''interest-rate increases are playing the largest role at this point'' in lifting home prices above the reach of many families, says Glenn Crellin, director of research information services for the NAR.

Rates on conventional fixed-rate loans requiring 20 percent down payments rose for five consecutive months through July and peaked at 14.68 percent in the week of Aug. 3. In the week ending Aug. 31, lenders were making commitments for such loans at 14.38 percent, according to the Federal Home Loan Mortgage Corporation. These figures understate what a borrower might have to pay, since they do not include closing costs or the price of private mortgage insurance.

Interest-rate forecasting is notoriously difficult, but DRI sees mortgage rates rising from 0.1 to 0.2 percentage points in the next six months, thus cutting even more families out of the housing market.

Some effects of higher mortgage rates are already being seen. In July, housing starts fell 6.6 percent from June, to a seasonally adjusted annual rate of 1.76 million. Starts of new single-family homes dropped 10 percent. And permits for new building, an indicator of future housing activity, were issued at a seasonally adjusted annual rate of 1.562 million in July, down 12 percent from June.

Higher mortgage rates caused sales of existing single-family homes to fall 6. 1 percent in July, to 2.78 million units, the third consecutive decline and the lowest level since November 1983, according to the NAR.

The July sales pace was 33 percent below the peak resale activity of 4.15 million units in November 1978.

The government said last week that sales of new single-family homes in July remained unchanged from the June level of 630,000 and slightly above the 606,000 sales pace of July '83. The affordability of new single-family homes was helped by a $2,200 price decline in July to $95,600. Housing affordability index

(An index of 100 means a family earning the national median income has 100 percent of the income needed to qualify for a mortgage covering 80 percent of the median resale price of homes for the period in question.)

1978 111.4 1979 97.2 1980 79.9 1981 68.9 1982 69.5 1983 83.2 1984 Jan 86.7 Feb 86.5 Mar 86.6 Apr 87.4 May 86.6 Jun 85.6 Jul 83.3

Source: National Association of Realtors