How does the sodium-potassium pump contribute to the net negative charge of the interior of the cell?

By moving three positively charged ions out of the cell for two positively charged ions entered.

Explanation:

The sodium-potassium pumps are the pumps located in the plasma membrane and are involved in the active transport of sodium-potassium ions. Binding of ATP and three sodium ions to the sodium-potassium pump is followed by hydrolysis of ATP and the use of released energy to bring about the conformational change in the shape of the pump.

This allows the bound three sodium ions to move out of the cell. As the sodium ions are released out of the cell, two potassium ions enter into the cell through the pump.

Since three positively charged sodium ions are expelled out of the cell for two positively charged potassium ions entering the cell, the net effect is making the interior of the cell negative with respect to its exterior.