– Consumers and companies are starting to act as if the economic expansion is here to stay.

Purchases of new homes jumped in May to a five-year high, while business investment plans improved for a third straight month, figures from the Commerce Department showed Tuesday in Washington. The last time households were this confident was in January 2008, according to another report.

The data point to the self-sustaining expansion the Federal Reserve is seeking to nurture as rising property values boost household wealth and spending, while businesses invest in new equipment to meet growing demand.

Stocks climbed, with the Standard & Poor’s 500 index rebounding from a nine-week low, as the figures supported forecasts the economy will overcome a midyear slump and accelerate in the second half of 2013.

“It’s all good news,” said Mark Zandi, chief economist at Moody’s Analytics in West Chester, Pa. “The economy is going to gain traction.”

Americans are gaining confidence as their biggest assets — their homes — become more valuable. The New York-based Conference Board’s consumer sentiment index increased to 81.4 in June from 74.3 a month earlier, data from the private research group showed.

Tuesday’s figures are in line with the Bloomberg Consumer Comfort Index, which has been hovering around a five-year high reached in late April. American households last week were the least pessimistic about the current state of the economy in more than five years, the Bloomberg index showed.

Spirits are lifting as employment picks up. The Conference Board’s survey showed more consumers thought opportunities will open up in the next six months and an increasing share said jobs were plentiful right now.

Houses aren’t the only thing consumers are more willing to buy as prospects improve. Cars and light trucks sold at a 15.2 million annualized rate in May, putting 2013 on course to be the best year for automakers since 2007, according to industry figures.

The gains in spending, which account for 70 percent of the economy, are helping to bolster the expansion after government budget cuts took effect in March.

“Unambiguously, the economy is showing signs of improvement despite sizable fiscal drag,” said Jim O’Sullivan, chief U.S. economist at High Frequency Economics in Valhalla, N.Y. Among the positives “has been the improving labor market, but in addition, wealth in general has been rising, at least up until the last week.”

The S&P 500 climbed 1 percent Tuesday to 1,588.03, while the Dow Jones industrial average rose 100.75 points, or 0.7 percent, to 14,760.31.

The Conference Board said the cutoff day for responses to be included in its report was June 13. Stocks have declined since then, with the S&P 500 dropping 2.5 percent on June 20, the biggest one-day sell-off since November 2011.

Growing demand for cars and trucks and gains in homebuilding are helping counter weakness in export markets, benefiting manufacturers such as BorgWarner Inc. and United Technologies Corp. Businesses may also decide to replace aging equipment, which will help bolster expansion in the second half of 2013.

Orders for durable goods, those meant to last at least three years, climbed a larger-than-projected 3.6 percent for a second month reflecting broad-based gains, according to figures from the Commerce Department.

Orders for non-defense capital goods excluding aircraft, a proxy for future business investment in computers, electronics and other equipment, climbed 1.1 percent in May after rising 1.2 percent and 1.1 percent in each of the prior two months.

Shipments of those products, a measure used in calculating gross domestic product, rose 1.7 percent, the biggest gain since November.

“This is the missing piece for an upswing in economic activity,” said Millan Mulraine, director of U.S. rates research at TD Securities USA LLC in New York. “Business capital investment activity is off to a strong showing. If businesses start investing, they’ll add to their workforce.”

Fed Chairman Ben Bernanke said last week that the central bank may begin to pare its $85 billion in monthly asset purchases this year if the economy performs as policymakers forecast. The process could be completed by mid-2014, by which time the jobless rate will probably have dropped to around 7 percent, he said.