Should any member die and not leave a beneficiary entitled to a pension under this article, such funds as he or she shall have paid into the pension fund at the time of his or her death shall be paid to such person as he or she shall have nominated by written designation duly executed and filed with the board. In no event shall such refund include accumulated interest on the member's contributions or any portion of the City's contributions to the pension fund. In default of the designation of the beneficiary, all payments made by a member and on his or her behalf by the City, together with accumulated interest, shall accrue to the pension fund. (Code 1979, § 15-103)