How much money should I have in hand for Fall 2016?

So this school I am considering is offering me $22765 in Grants/scholarships and $5500 in direct unsubsidized and subsidized loans, for a total of $28265. The cost of Attendence is $41394. Broken down, it is $28638 in tuition; $10108 in room/board; $950 in books (which I could reduce if I rent/use discount or used books); $1634 in personal charges.

Now, if I applied all of my grant/loan money, I can completely knock out the tuition, leaving me with $12756 dollars to come up with. Do I need the majority of this extra money right when I start school in the Fall, or can I work while in school to make up this portion? I planned on working in the Summer which I could make about $2000-$4000 during my 11 weeks before school starts, meaning I only have about $10756-$8756 leftover to pay. Is this sum something I can pay off through working or do I need this money immediately?

If I can pay this through working, here is what my plan was. My mother said she would be able to give me like $50 each week, which adds up to $2600 a year ($8756-6756 left). I was offered $3500 in work study money ($5756-$3756). I could probably get another job to float the leftover $5756-$3756. Does this sound viable or am I making some sort of error somewhere?

How does the school bill? If the school bills on a semester basis, you will probably receive your first bill in mid-summer that will cover fall semester 2016. That bill will have half the tuition, half the fees and half the room and board as charges, offset by half of the grants/scholarships and half of the total loans. The balance will be your responsibility to pay before the due date, plus you will need to come up with money at the beginning of the semester for books and any required supplies, and then money throughout the semester for personal expenses.

@BelknapPoint I would be billed for the Fall semester in August (amount due by the 22nd) and for the Spring semester in January (again, due by the 22nd). If I cannot pay the full amount in August, I can enter a deferred payment plan where I am billed August, September, and October with 3 payments equaling the total due. For the Spring semester I would pay 3 smaller charges for January, February, and March.

Bump