To cause to be actuarially determined the unfunded liability existing in the Fund as of the date provided by subsection (c) of Section 5-1 of the School Code by reason of annuities and other benefits payable and to become payable from the Fund to persons specified in that subsection with respect to periods of service ending on or before that date, to report the amount so determined to each school board required under that subsection to pay a proportionate share of that amount to the Fund, and to receive and apply in accordance with this Article all amounts so paid to the Fund by those school boards.