Converting Dates Into A Days Remaining List

So I currently have a document that is listed for aircraft maintenance schedules. I need to make the excel doc show us the hours remaining for things that are hourly time items and the days for things that are by date items. I have an example in front of me that does just that, but I do not know how to write out the functions (as in the example is printed).

I have a column showing "Day Limit" (ie: 365, this is a permanent entry that doesn't change, though some items have different limits, naturally) and then a column showing "Date Complied With" (this is the only user entered value). I want these to produce me a column that shows me "Next Due Date" is (such as "07/24/13" form or similar), and finally a column showing how many days until that date (subtracting the "Next Due Date" column from today's date and giving me a single "Days Remaining" value, (so it would display "13" if using the previous date).

If you would like me to upload a dummy copy then I can, but I feel like that was about as explanatory as you could need haha. I have all of the hourly limits figured out, those were obviously very simple addition and subtraction formulas. This has me a little stumped and so far google has not been much help...

Thanks a lot.

Edit: Okay so the first part was way easier than I realized and I'm slightly embarrassed I didn't get it immediately haha. Getting it to display the "Date Due" column is now finished, I just need the "Days Remaining" solved.

Thank you for providing the solution. In future, you can post your solution as post 2 so its clear to others which is the question and which is the solution.