Stocks soared higher on Tuesday, pushing the S&P 500 Index (SPY  ) and Nasdaq Composite (QQQ  ) each to fresh record highs, after a softer-than-expected inflation report eased some fears regarding President Donald Trump's tariff policies and further fueled expectations that the Federal Reserve would interest rates at its September meeting.

The broader market index rose 1.13% on the day to settle at 6,445.76, while the tech-heavy index advanced nearly 1.4% to close at 21,681.90 for the first time. The Dow Jones Industrial Average (DIA  ) also jumped over 480 points to end at 44,458.61.

Capturing much of investors' attention, consumer prices accelerated at a less-than-expected pace in July, as the start of Trump's tariffs on major trading partners showed little impact on American wallets.

The consumer price index rose by a seasonally adjusted rate of 0.2% month-over-month and 2.7% annually in July, the Bureau of Labor Statistics reported Tuesday, with the 12-month basis coming in slightly below economists estimates from Dow Jones for a 2.8% increase.

Excluding food and energy prices, so called core CPI rose by 0.3% on the month and 3.1% from a year ago, with the annual reading slightly topping estimates for an increase of 3%. Moreover, the monthly core rate gain was also the largest since January.

"Inflation is on the rise, but it didn't increase as much as some people feared," said Ellen Zentner, chief economic strategist for Morgan Stanley Wealth Management, quoted by CNBC. "In the short term, markets will likely embrace these numbers because they should allow the Fed to focus on labor-market weakness and keep a September rate cut on the table. Longer term, we likely haven't seen the end of rising prices as tariffs continue to work their way through the economy."

Still, the reading reassured market participants that Trump's tariffs will have little immediate impact on the economy, especially as the White House extended the deadline on higher tariffs for Chinese imports by another 90-days on Monday. Traders are now pricing in a more than 90% chance the central bank will reduce its target range for its benchmark interest rates by 25-basis-points next month, according to CME Group's FedWatch tool -- up from 85% before the data release.

U.S. small-business sentiment rose higher in July, the National Federation of Independent Business reported Tuesday, even as owner outlook continued to dim as macroeconomic and labor conditions weakened. The firm's Small Business Optimism Index gained 1.7 points to 100.3 last month, while the survey's Uncertainty Index rose by 8 points to 97 as "clouding decisions about hiring, pricing, investment in plant and equipment" impacted forecasts.

"While uncertainty is still high, the next six months will hopefully offer business owners more clarity, especially as owners see the results of Congress making the 20% Small Business Deduction permanent and the final shape of trade policy," said Bill Dunkelberg, chief economist at NFIB, in a statement. "Meanwhile, labor quality has become the top issue on Main Street again."

Elsewhere, Intel (INTC  ) shares climbed higher on Tuesday after Trump reversed his previous stance on CEO Lip-Bu Tan, calling the semiconductor leader's career "an amazing story" after meeting with him along with Commerce Secretary Howard Lutnick and Treasury Secretary Scott Bessent on Monday. Last week, Trump called Tan "highly CONFLICTED" and said he must resign from his position "immediately," adding that there was "no other solution to this problem."

Intel said in a statement late Monday that the meeting between Tan and the White House was a "candid and constructive discussion on Intel's commitment to strengthening U.S. technology and manufacturing leadership," and plans to work closely with the Trump administration to "restore this great American company."

Looking ahead, traders will pay close attention to Thursday's producer price index report for more clues on wholesale inflation ahead of the Fed's Jackson Hole summit at the end of the month.