After consulting the retirement system's actuary, the department of management and budget shall calculate for each fiscal year any cost savings that have accrued to this state as a result of the implementation of 1996 PA 487 over the costs that would have been incurred by this state to fund this retirement system had 1996 PA 487 not been implemented. For each fiscal year in which a deposit under section 38(6) does not occur, the department may deposit all or part of the cost savings calculated pursuant to this section into the health advance funding subaccount created under section 11(9) by reducing the normal cost and unfunded actuarial accrued liability contribution rates as calculated pursuant to section 38, and increasing the contribution rate for benefits provided under section 20d by the same amount. However, the normal cost and unfunded accrued actuarial liability rates shall not be reduced to an amount less than zero.