N.C. Gen. Stat. § 42-6

In all cases where rents, rent charges, annuities, pensions, dividends, or any other payments of any description, are made payable at fixed periods to successive owners under any instrument, or by any will, and where the right of any owner to receive payment is terminable by a death or other uncertain event, and where such right so terminates during a period in which a payment is growing due, the payment becoming due next after such terminating event shall be apportioned among the successive owners according to the parts of such periods elapsing before and after the terminating event.