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It appears that the first electric fund transfers using a computer occurred in 1966.
Third-generation or integrated-circuit-based computers were associated with electronic commerce technologies such as automatic teller machines, electronic funds transfer, stock market automation, facsimiles, email, point of sale systems, electronic bulletin boards and electronic data interchange. In 1965, automated teller machines were created [23], which were electronic machines or computers that automatically dispense money or cash [22]. In 1966, electronic funds transfer or EFT was created [24], which was βa set of processes that substitutes electronic messages for checks and other tangible payment mechanismsβ
For further reading on its usage.