The state of Rhode Island shall make its contribution for the maintaining of the system established by § 8-8-10.1 and providing the annuities, benefits, and retirement allowances in accordance with the provisions of this chapter by annually appropriating an amount that will pay a rate percent of the compensation paid after December 31, 1989, to judges engaged after December 31, 1989. The rate percent shall be computed and certified in accordance with the procedures set forth in § 36-8-13 and § 36-10-2 under rules and regulations promulgated by the retirement board pursuant to § 36-8-3 and shall be transmitted on the date contributions are withheld but no later than three (3) business days following the pay period ending in which contributions were withheld.