In the event a retirant dies before he has received in allowance payments an aggregate amount equal to his accumulated contributions standing to his credit in the members deposit fund at the time of his retirement, the difference between such accumulated contributions and such aggregate amount of allowance payments received by him shall be paid to such person as he shall have nominated by written designation duly executed and filed with the board. If there be no such designated person surviving such retirant, such difference, if any, shall be paid to the retirant’s estate. In no case shall any benefits be paid under this section on account of the death of a retirant if any allowance becomes payable by the system on account of his death.