(a) Except as otherwise provided in this section, if a person or governmental unit fails to pay a tax imposed under this article on or before the date on which the tax is due, the tax collector shall assess interest on the unpaid tax from the due date to the date on which the tax is paid.

(b) Except as provided in subsections (c)(2) and (d) of this section, the date on which the tax is due is determined without regard to any extension of time to file a return.

(c) Interest on unpaid inheritance tax begins:

(1) 30 days after the date on which the tax is determined;

(2) on the original due date, if there is no formal administration of the estate and the tax is not paid within 30 days after the date on which the tax bill is mailed; or

(3) 30 days after the original due date, if an alternative payment schedule for inheritance tax is allowed.