http://www.bc.edu/offices/stserv/financial/finaid/undergrad/how_aid_works/cost_of_attendance.html
The ‘padding’ talked about are estimates for books, supplies included in COA but not direct billed costs. These can be on the high side and differ between colleges.
The $71,000 number from BC is their COA for 201/18.
The estimate you got in your aid award might have been for 2016/17.
Costs can go up every year.
Room and board depends on options ultimately chosen.
BC
2017/18
Direct costs:
Tuition $52,500
Fees $1,401
R&B $14,142
Total $68,043
Aid:
Scholarship $56,600
SEOG $400
Pell $1,670
$58,670
Net price:
$9,373
Subsidized loan offered:
$3,500
Remaining cost: $5,813
Lehigh
I’m assuming those are 2017/18 estimates since the website shows tuition of $47,900 for 2016/17
Tuition $50,320
Fees $1,170
R&B $13,120
Total $64,610
Aid:
Lehigh Grants
$53,010 + $3,500 = $56,510
Pell 1,670
$58,180
Net price:
$6,430
Subsidized loan offered: $2,006
Remaining cost: $4,424
You will also need some money for travel, books and supplies for first semester.
I did not include work study income in the calculation, it is not available up front, and will be earned depending on hours worked.