"you have finished your first Game Java applet in a very professionally accepted and methodical way"

Please tell me you are joking.

System resource use is amazingly high due to that while loop which does not even need to be there.
The timer is already polling every 15ms, you don't need the while loop also.

I suggest making the Timer an instance variable and ending the start method at time.start();

This way your actionPerformed can look like this:

  public void actionPerformed(ActionEvent arg0) 
            {
                if(pRight.getScore() == 10)
                 {
                    time.stop();
                    currentTime = System.currentTimeMillis() - currentTime;
                 }
                 else
                 {
	         //moves the ball
	         ball.move();
	         //lines the computer paddle up with the ball
	         pRight.setPos(ball.getY() - 35);
	         //checks the ball for a collision
	         checkCollision();
                 }


	         //repaints the applet
	         repaint();
	    }

Much more efficient.