When a limitation or period of time prescribed in any act in effect on December 31, 1987, for acquiring a right, barring a remedy, or for any other purpose has begun to run before January 1, 1988, and when a limitation or period of time is prescribed in this Code for acquiring the right, barring the remedy, or for any other purpose, then the time which has already run shall be deemed to be part of the time prescribed by the limitation or period in this Code.