We apply the nonequilibrium Green's function formalism to the problem of a multiterminal nanojunction subject to an arbitrary time-dependent bias. In particular, we show that taking a generic one-particle system Hamiltonian within the wide-band-limit approximation, it is possible to obtain a closed analytical expression for the current in each lead. Our formula reduces to the well-known result of Jauho et al. [Phys. Rev. B 50, 5528 (1994)] in the limit where the switch-on time is taken to the remote past, and to the result of Tuovinen et al. [Phys. Rev. B 89, 085131 (2014)] when the bias is maintained at a constant value after the switch-on. As we use a partition-free approach, our formula contains both the long-time current and transient effects due to the sudden switch-on of the bias. Numerical calculations performed for the simple case of a single-level quantum dot coupled to two leads are performed for a sinusoidally varying bias. At certain frequencies of the driving bias, we observe “ringing” oscillations of the current, whose dependence on the dot level, level width, oscillation amplitude, and temperature is also investigated.