| The difference between the 5,000 and the 3,117 is mostly related to federal and state taxes that the employer withheld and paid over to the government on your behalf. As a result, when you file your tax returns you will be able to claim these amounts as tax payments against your tax.
For example, if you owe no tax for the year, then the entire amounts that your employer withheld and paid to the government will be refunded to you when you file your tax return.
I am not sure, but you might even be able to get a refund of the social security/medicare taxes that were withheld. Without looking at your pay stubs it is impossible to tell if there were other amounts that you will not get back. Generally though, your employer is right that you should pay the full amount (or likely something close to it).
If your employer did not pay you for any relocation expenses, then you should not have to reimburse the employer. |