(b) If there be no surviving spouse at the time of death of a judge who dies after serving five years or more as a sitting judge of any court of record and such judge leaves surviving him any dependent child or children, such dependent child or children shall receive an amount equal to twenty percent of the annual salary of the office which said judge held at the time of his or her death: Provided, That the total of all such annuities payable to each such child shall not exceed in the aggregate an amount equal to forty percent of such salary. Such annuity shall continue as to each such child until: (i) He or she attains the age of eighteen years; or (ii) attains the age of twenty-three years so long as such child remains a full-time student. The Auditor shall by legislative rule establish the criteria for determining a person's status as a full-time student within the meaning and intent of this subsection. In the event there are surviving any such judge three or more dependent children, then each such child's annuity shall be proratably reduced in order that the aggregate annuity received by all such dependent children does not exceed forty percent of such salary and the amount to be so received by any such child shall continue throughout the entire period during which each such child is eligible to receive such annuity. The provisions of this subsection shall also apply to those circumstances and situations wherein a surviving spouse of a deceased judge shall die while receiving benefits pursuant to subsection (a) of this section and who shall leave surviving dependent children of such deceased judge who would be entitled to benefits under this subsection as if they had succeeded to such annuity benefits upon the death of such judge in the first instance. In the event the salary of judges is increased or decreased while an annuitant is receiving benefits pursuant to this subsection, the annuities payable shall be likewise increased or decreased proportionately to reflect such change in salary: Provided, however, That with respect to any individual who is appointed or elected for the first time as judge of a court of record of this state after the first day of July, two thousand five, any annuity to any children of the judge shall be calculated with respect to the judge's final average salary: Provided further, That the child is not entitled to an increase in benefits by virtue of any increase in the salaries of the offices of circuit court judge or Justice of the Supreme Court of Appeals. The annuities granted hereunder shall accrue monthly and shall be due and payable in monthly installments on the same day as surviving spouses' benefits are required to be paid. Such annuities shall commence on the first day of the month in which any such dependent child becomes eligible for benefits hereunder and shall terminate on the last day of the month during which such eligibility ceases.