@LovelyAshley the best thing you can do to convince your parents is show them the breakdown and what you’re willing to do to cover the rest. I think that if you show you’re serious and that you thought out your plan there isn’t much else they can say. In my opinion, if you show them all the figures I mentioned before (plus the breakdown I’ll mention here) and tell them how easily you can pick-up the rest of the tab with work, if they STILL don’t get on board I don’t think they ever will. I mean, did they ever tell you they can do the EFC of $10,000 a year? If so, I don’t see why they have an issue with it this time if you’re able to pay the rest yourself. Perhaps they don’t want you working? Or maybe they don’t like the idea of school on the east coast?
Now, @mommymetal is right in that you need to know how much you’re actually paying for the school. I might not have explicitly said it, but that’s why I tried to do in my first post. What you HAVE to pay the school is:
**Tuition: $48,700/b,
Fees: $410
**Room and board: $11,750-14,040/b
Total: $60,860
Extra expenses that you ‘pay-as-you-go’:
Books & supplies: $1,275
Personal: $1,475 (what the university calls laundry, entertainment, etc. Technically, this can be covered under part of your Colonial Cash/meal plan as $1,400 of the $3,600 goes to food while the other $2,200 can be spent on anything, like laundry or snacks
**Transportation: $1,000/b
*Total: $2,275/i
Some links to the above figures before I go on:
Costs of Attendance http://undergraduate.admissions.gwu.edu/costs-attendance
Housing for Freshmen https://living.gwu.edu/sites/living.gwu.edu/files/downloads/First%20Year%20Rate%20Chart%2015-16.pdf
Meal Plan http://www.gwcampusdining.com/plans/index.html
So, the total that you will pay over the course of the year is $63,135. Subtracting your FinAid package of $46,000 and EFC of $10,000 leaves $7,135. Only $4,860 of that goes to the school, which can go into a monthly (if you choose) payment plan over the course of the year. That comes out to roughly $540/mo due to the school, paid by YOU, not your parents. The other $2,275 is your books and flights, which can be paid in chunks (right before each semester, for example). You can either pay these with money you earn over the summer from a summer job or some other source.
Now, like @GWU2018 said, you can possibly stay-on with your Federal Work Study job after you make the $2,200 they offered you. That will save you the search for a new job (in case your parents worry about your ability to find something). I’m not sure what they pay hourly, but you can read more about them here http://careerservices.gwu.edu/federal-work-study-program. But even if you get a non work-study job, most of what I showed you paid $11/hr. A 15-hour week (very manageable with a full course load) would net you $660/mo before taxes. If you do 20-hour weeks (still very manageable- I did this as did my friends) it’s $880/mo before taxes.
As you can see, you can definitely make the $540/mo you’ll owe the school from a job on campus. In fact, there are all kinds of jobs OFF campus that you can make more than $11/hr, greatly increasing your monthly income (my two off-campus jobs were $16 and $17/hr, for example). If you factor in the money you can make over the summer you shouldn’t have any problem paying for everything you need for school.
From sophomore year on, like @mommymetal said, housing will go up. Second-year housing prices can be found here: https://living.gwu.edu/sites/living.gwu.edu/files/downloads/Second%20Year%20Rate%20Chart%2015-16_1.pdf. It can be anywhere from $2-6,000 more than freshman year. Your meal plan will go down $1,100, though, to $2,500. Now, while the $6,000 increase in housing sounds scary, just know that price increases come from nicer housing options OR smaller room sizes. If you have a budget in mind you can totally pick something more affordable. GW students typically try to spring for the fancy stuff anyway, so the “budget” options are almost always available 
While the though of housing increasing might be alarming, just know that it doesn’t go up for junior and senior housing. Just remember, you can always try for the RA position to obtain free housing. I’d even suggest asking around to see if there are other positions at GW that give a discounted housing rate (some jobs might have this as a perk).
Good luck with convincing the parents. I think that as long as they can keep an open mind and you’re able to sell your ability to cover the additional $7,135 yourself, you have a strong chance at them going along with GW 
Just keep us posted. I’d like to know if my super long posts paid-off, lol.
