The Aharonov-Bohm effect is investigated in two-dimensional, single-terminal quantum rings in magnetic fields by using time-dependent density-functional theory. We find multiple transport loops leading to the oscillation periods of h/(en), where n is the number of loops. We show that the Aharonov-Bohm oscillations are relatively weakly affected by the electron-electron interactions, whereas the ring width has a strong effect on the characteristics of the oscillations. Our results propose that in experimental quantum-ring devices showing clear Aharonov-Bohm oscillations the electron current is dominated by a few states along narrow conduction channels.