Generally speaking, the previous owner is responsible for her share of the proprortionate share of the property taxes for the period of time that she was in possession of the home. You take the number of days in possession divided by the number of days in the year and multiply it by your actual tax bill for 2007 to figure out the previous owner's share.
In the normal course, these calculations are done before you take possession in order to determine the cash to close. Things can get a bit complicated in these calculations depending on whether the actual tax assessment is known, whether the previous owner was paying monthly on TIPP or if the entire bill is due in one lump sum at the end of June.
It's entirely possible that you were given a credit for the previous owner's share of this year's property taxes and you will be responsible to pay the entire bill when it comes due at the end of the month. Check with the lawyer (or most likely, his/her assistant) that worked on your deal.
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