(a) Every retirant of the fund who is fifty-five years of age or older and who is retired by the board under the provisions of section twenty-seven of this article; every retirant of the fund who is retired by the board under the provisions of section twenty-nine or thirty of this article; and every beneficiary receiving a benefit pursuant to section thirty-three or thirty-four of this article is eligible to receive an annual retirement annuity adjustment equal to three and seventy-five hundredths percent of his or her retirement award or beneficiary award. The adjustments may not be retroactive. Yearly adjustments shall begin upon July 1, of each year. The annuity adjustments shall be paid to the retirants or beneficiaries from the fund in equal monthly installments while in status of retirement or payment of beneficiary award. The annuity adjustments shall supplement the retirement awards and benefits as provided in this article.
(b) Any retirant or beneficiary who receives a benefit pursuant to the provisions of section twenty-nine, thirty, thirty-three or thirty-four of this article shall begin to receive the annual annuity adjustment one year after the commencement of the benefit on the next July first: Provided, That if the retirant has been retired for less than one year or if the beneficiary has been in receipt of beneficiary payments for less than one year when the first annuity adjustment is given on that July first, that first annuity adjustment shall be a pro rata share of the full year's annuity adjustment.