One more type of story you can tell in a cover letter is the future story that address employer needs and challenges and tell how you would address those issues, as in these examples:
When I interviewed Ms. Kirkwood six months ago to obtain information about a career in real estate, she mentioned that the agency would like to establish a Web presence. I’d like to combine my interest in real estate with my knowledge of Web-page design and HTML programming to help you create a Webmaster position in your office. I’ve even sketched out some preliminary ideas on what your Web page might look like, and I’d love to get together and show them to you.
Because I recently assisted in managing one of the convenience stores in your company’s chain, I am well-acquainted with how to prioritize tasks. I oversaw organization of the employee task list. While corporate headquarters provided the basic structure of the task list, I modified it to meet our store’s needs. Now, I’d like to do that for all the corporate stores. Working in “the problem store,” as you often called it, I am certainly aware of the difficulties, and I have some ideas about how to solve them.
I understand that Hanover Information Systems deals heavily in telemarketing and database outsourcing. Maintaining a database can be very expensive for a company, and outsourcing this task can sometimes be more efficient. I am confident that I can help increase the company’s productivity by creating optimal ways to maintain the databases.
Tell Me About Yourself: Storytelling that Propels Careers, Quintessential Careers Press, ISBN-10: 1-934689-00-9. Find out the ways you can own the entire book.

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