(a) In the case of employers participating on July first, nineteen hundred forty-eight, the rate of such contribution shall continue to be the rate theretofore determined pursuant to law. Such rate may be varied, however, if an adjustment is necessitated by reason of the allowance of additional prior service credits.

(b) In the case of an employer electing to participate after July first, nineteen hundred forty-eight and before March thirty-first, nineteen hundred ninety-nine, an initial actuarial valuation shall be made to determine the accrued liability of such employer by reasons of the prior service of those of its employees who are members of the retirement system. The rate of deficiency contribution for such employer shall then be determined. Such rate shall be that proportion of the total annual compensation of such employees as is equivalent to four per centum of such accrued liability. Such rate shall be applied to the employer's payroll of members, as used in the annual valuation. The cost of making such initial valuation shall be assessed against and paid by such employer. Notwithstanding the above, for employers who commence participation in the retirement system on or after April first, nineteen hundred ninety-nine, the accrued liability shall be amortized in equal annual installments over a twenty-five year period. With respect to such employers the cost of making such initial valuation shall be assessed against and paid by the employer. The provisions of subdivisions c, d and e of this section shall not apply to employers who commence participation in the retirement system on or after April first, nineteen hundred ninety-nine.

(c) The amount of each annual deficiency contribution payable by every employer shall be at least three per centum greater than the amount for the preceding year.

(d) The comptroller shall approve the discontinuance of the state's deficiency contribution on account of members employed by it when:

(1) The total amount in the pension accumulation fund on account of all members, and

(2) The present value of future deficiency contributions still to be paid by other employers, and

(3) The present value of future normal contributions, on the basis of the rate of normal contribution then in effect, shall equal the then present value of the total liability of such fund on the basis of the tables then in use.

(e) Unless previously discontinued, or unless hereafter discontinued pursuant to other provisions of law, the deficiency contribution of a participating employer shall be discontinued when the total amount of deficiency contributions paid by such employer at least equals or shall hereafter equal such percentum of its initial accrued liability computed by the actuary as shall equal that percentum of the state's initial accrued liability paid by deficiency contributions during the period equal to the period last determined by the actuary as the deficiency payment period. Nothing herein contained shall be deemed to give any participating employer any valid claim or cause of action for refund or credit for any sum or sums paid or to be paid for fiscal years prior to and including the fiscal year ending March thirty-first, nineteen hundred sixty-six nor to excuse any participating employer from the payment of any contributions for such fiscal years. 3. Administration contribution.

(a) The expenses of the retirement system, including an amount allocated to amortize over a period of thirty years, with interest, the cost of construction of the retirement system building, and the cost of maintenance of such building, for each fiscal year shall be determined at the close of each such year. The ratio of such expenses to the total compensation of all members, as used in the actuarial valuation, shall be the rate of such administration contribution. Such rate shall be applied to each employer's payroll of members, as used in the annual valuation.

(b) All such expenses shall be paid out of the pension accumulation fund which shall be reimbursed through administration contributions and other monies received from employers pursuant to this article.

(c) Notwithstanding any other provision of this subdivision or any other law, the administrative contribution for a year, as determined pursuant to paragraph one of subdivision b of this section, shall be paid from the pension accumulation fund if payment from such fund will not affect the normal contribution for such year. c. Additional contributions shall be made in accordance therewith by employers obligated to contribute to the retirement system pursuant to any other section of this article. d. When a pension or a pension-providing-for-increased-take-home-pay, if any, becomes payable to or on account of any member, a reserve, in an amount computed by the actuary to be necessary to provide the pension or pension-providing-for-increased-take-home-pay, if any, granted in each such case, shall be transferred from the pension accumulation fund to the pension reserve fund. e. Whenever the comptroller, upon recommendation by the actuary, shall determine that it is necessary to increase the reserves held in the annuity reserve fund or the pension reserve fund, he may direct that the amount so needed shall be transferred thereto from the pension accumulation fund. f. The amount of regular interest which is to be credited to the annuity savings fund, the annuity reserve fund and the pension reserve fund, and the amount of special interest, if any, which shall be credited to the annuity savings accounts in the annuity savings fund, shall be determined after the close of each fiscal year. Each such amount thereupon shall be transferred from the pension accumulation fund to each such fund.