Interviewing and on-boarding is a costly and time consuming process for any company and hiring manager. Assure the interviewer that you are seeking a long term fit with your next employer.
Take a look at the career growth options with the company. If any of these stand out to you, it's a great idea to specifically mention them to the interviewer. Your expressed interest in those particular internal opportunities will solidify the fact that you are, indeed, seeking a long term fit with them.
"I am looking for a long-term fit in my next position. As you can see, I had strong progress and career growth in my previous company. I would love to see the same success with your company. I did notice on your website that you have global leadership opportunities. If I could work my way into a role like that, I would be thrilled."
Second Answer Example
"Long range, I would like to see myself making strong progress towards a leadership role with Paychex Inc.. I sincerely hope this can happen within your organization as I understand that you choose to promote from within wherever possible."