Stocks jumped Tuesday after Chinese President Xi Jinping said Beijing would reduce tariffs on imported cars and improve intellectual property protection, steps that could ease trade tensions. Facebook climbed as CEO Mark Zuckerberg testified before the Senate about the company’s privacy scandal.

On Tuesday:

The S&P 500 index climbed 43.71 points, or 1.7 percent, to 2,656.87.

The Dow jumped 428.90 points, or 1.8 percent, to 24,408.

The Nasdaq composite rallied 143.96 points, or 2.1 percent, to 7,094.30.

The Russell 2000 index of smaller-company stocks soared 28.97 points, or 1.9 percent, to 1,543.43.

For the week:

The S&P 500 is up 52.40 points, or 2 percent.

The Dow is up 475.24 points, or 2 percent.

The Nasdaq is up 179.19 points, or 2.6 percent.

The Russell 2000 is up 30.14 points, or 2 percent.

For the year:

The S&P 500 is down 16.74 points, or 0.6 percent.

The Dow is down 311.22 points, or 1.3 percent.

The Nasdaq is up 190.91 points, or 2.8 percent.

The Russell 2000 is up 7.92 points, or 0.5 percent.