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See NAT Gateway pricing info here: https://aws.amazon.com/vpc/pricing/.
When will direct billing (though KFS) based on "cost_center" tags be released?
This is still a work in progress and we expect to release this Cornell KFS feature in Spring 2017. In the meantime, you should strive to add "cost_center" tags to your AWS resources as soon as possible. See Standard Tagging for details.
Until direct billing is turned on, you can use CloudCheckr or our billing API to sub-total the resource costs in your account (based on tag) and re-allocate those costs with the help of your unit Business Service Center.