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The ability of the typical American family to buy a previously owned home fell for a second straight quarter from April through June as mortgage rates continued to rise, a real estate trade group said Tuesoday.

The National Association of Realtors said its Housing Affordability Index slipped 6.7 percent to 131.2 from 140.6 during the January-March quarter.The index had reached 141.9 in the final three months of 1993, the second-highest since it hit 145.1 in the second quarter of 1973. But it then slipped 0.9 percent in the next three months as rates rose.

When the index measures 100, a family earning the national median income has exactly the amount needed to purchase an existing home at the national median price, using conventional financing and a 20 percent down payment.

Since the median is the midpoint, the composite index for the April-June quarter means that half of American families had at least 131.2 percent of the income needed to qualify for the purchase of a median-priced home costing $110,600.

In fact, since the median family income was $38,651, the typical family could afford a $144,900 home.

But despite the increase in mortgage rates, the index was little changed from 133.1 during the same period last year.

According to the Federal Housing Finance Board, rates averaged 7.42 percent in the second quarter, up from 6.91 percent in the January-March quarter and 7.26 for the same period last year.

The Realtors also said its index measuring the purchasing power of first-time home buyers also fell for a second straight quarter, down 6.8 percent to 85.3. This index, which reached 92.3 in the final three months of 1993, slipped 1 percent during the next quarter.

The first-time index shows the ability of renters who are prime potential first-time buyers to qualify for mortgages on starter homes. When it equals 100, the typical buyer can afford a typical starter home under existing financial conditions with a 10 percent down payment.