We present an approach for time-dependent quantum transport based on a self-consistent nonequilibrium Green function formalism. The technique is applied to a ballistic carbon nanotube transistor in the presence of a time-harmonic signal at the gate. In the on state, the dynamic conductance exhibits plasmonic resonant peaks at terahertz frequencies. These vanish in the off state, and the dynamic conductance displays smooth oscillations, a signature of single-particle quantum effects. We show that the nanotube kinetic inductance plays an essential role in the high-frequency behavior.