Answer:
Home owner's exemption is not the same as homestead exemption. Depending on the state that you live, homestead can be up to $50,000 of the home's value, but homeowner's exemption is generally up to $7,000 only. This means that the buyer's basis will lower by $197,500 - $7,000 = $190,500.
Assuming that the real estate tax rate is 1%, then the new tax bill (including homeowner's exemption) would be $190,500 x 1% = $1,905.