If I read 40 pages per day for the next 4 months will I see an improvement in my vocabulary?
You sure will! But if you really want to improve your vocabulary, read so-called English Literature some of the time. This, in the broad sense, includes American Literature at the very least. I don’t want to run through a list of all the English-speaking countries (including India, which has a genuine literature in English), but they would all be on it. The reason I suggest this is because of a basic principle in foreign-language teaching which applies to us native speakers too: the most improvement comes from giving a student what he or she already knows plus alpha (alpha being what the student doesn’t know; it should be a fraction of the book read). When I read my first 19th-century novel on my own, as (in public school terms) a first-year high school student, my vocabulary shot up. It was “Jane Eyre,” and though I was a guy, I came to just love it. But I needed to use a dictionary at first. By the end of the novel, I didn’t need the dictionary. So all reading of decent writing is good for your vocabulary, but something fine and a little challenging (with the plus-alpha factor) is best.