At the last meeting of the council in each month, the treasurer shall present a list of the persons as shown by the record in his office, entitled to pensions[,] the amount payable to each such person. The council shall examine such list and if found to be correct, shall order the payment of moneys due all such persons. A warrant shall be drawn, for the payment to each person entitled to such moneys ill the same manner as is provided for the payment of all other claims against the city. Such pensions shall be paid out of the firemen's and policemen's pension fund.