(b) In the event a member dies and does not leave a beneficiary entitled to an annuity payable by the retirement system, his accumulated contributions standing to his credit in the members deposit fund at the time of his death shall be paid to such person or persons as he shall have nominated by written designation duly executed and filed with the board of trustees. If there be no such designated person or persons surviving the said member, his said accumulated contributions shall be paid to his estate.
(c) Refunds of a member's contributions or accumulated contributions, as the case may be, may be made in equal installments according to such rules and regulations as the board of trustees may from time to time adopt.
(d) In the event a member dies and a refund of his contributions is due to be made to an infant child or children by reason of being the person or persons nominated by written designation duly executed and filed with the retirement system, and the amount of said refund is less than one thousand dollars, then, and in said event, the board of trustees may make said refund, upon written application, to the closest relative or natural guardian for the use of said infant child or children. The board of trustees may, at its discretion, require that said relative or natural guardian post bond with the retirement system to insure that said money will be used for the benefit of said infant child or children. In any event, before said refund is made to said relative or natural guardian of the said infant or infants, said relative or natural guardian shall give the retirement system an indemnifying release of said sums so paid over.