An index of American mortgage applications fell last week as higher borrowing costs made it less profitable for homeowners to refinance. Home purchases increased.

The Mortgage Bankers Association’s measure of applications fell 0.3% to 752.1 in the week ended July 29, from 754.3.

The level was the lowest since the last week of May. The average rate on a 30-year fixed mortgage rose to 5.83%, the highest since the middle of April.

The rise in interest rates, up in four of the last five weeks, pushed the group’s gauge of refinancing down 3% to 2250.3, the lowest level in two months. The decrease removes a source of support for consumer spending and the economy.

“Business is slowing a little bit, coming off the super-heated times we had the last month and a half,” the chief economist at Quicken Loans, Bob Walters, said. “It’s still strong, but not as strong as we’ve seen in the last few weeks as interest rates have come up a bit.”

Mortgage refinancing in which borrowers received cash rose 25% in the second quarter, according to a report from Freddie Mac, the no. 2 mortgage financier. The share of all refinancing loans that were so-called “cash-out refis” was 74%, a 4 1/2-year high.

About one-third of the cash extract ed from home equity is used for home renovations, another third is used for debt repayment, and the rest is spent on items such as cars and vacations, the chief economist for Freddie Mac, Frank Nothaft, said.

Personal spending adjusted for inflation rose 0.8% in June, the biggest increase since July 2004, the Commerce Department said on Monday.

The average rate on a 30-year fixed mortgage increased from 5.72% in the week ended July 22. Average rates on the 15-year fixed and 1-year adjustable mortgages also rose last week.

While borrowing costs are beginning to rise, the rate on a 30-year fixed mortgage is 14 basis points lower than it was at the same time last year. A basis point is one-hundredth of a percentage point.

Mr. Walters said Quicken is seeing some customers refinance to fixed-rate mortgages from their current adjustable-rate mortgages because they want to avoid the risk of having to refinance later on a higher rate.

The share of applications for adjustable-rate mortgages fell to 28.5%, from 29.4%. The one-year adjustable rate mortgage rose to 5.03% from 4.95%, while the average on a 15-year loan rose to 5.7 % from 5.61%.

At the current 30-year fixed rate, every $100,000 of a mortgage would cost a homeowner $603.41 a month. When the rate was at a four-decade low of 4.99%, costs were $536.21.

The group’s index of applications to purchase homes rose 1.7% to 540 from 521.2 the previous week.

“The housing sector of the economy is still doing quite well,” a senior economist at JPMorgan Asset Management, Anthony Chan, said. “Over the next couple of months, it’s very hard to see any weakness in any of the components that drive the housing market.”

The refinancing gauge fell from 2320.3 in the prior week.

The last time the level was so low was the week ended May 27, when it was 2142.1. The refinancing index is still higher than it was a year ago. The share of applications for refinancing fell to 41.7% last week, from 42.9%.

The Mortgage Bankers Association survey covers about half of all American retail residential mortgage originations and has been conducted weekly since 1990.