A numerical study of size-dependent effects in thermodynamics of a small droplet formed around solid nanoparticle has been performed within the square-gradient density functional theory (DFT). The Lennard-Jones fluid with the Carnahan-Starling model for the hard-sphere contribution to intermolecular interaction in liquid and vapor phases and interfaces has been used for description of the condensate. The intermolecular forces between the solid core and condensate molecules have been taken into account within the model of the total molecular potential of the core. The influence of the electric charge of the particle has been considered under assumption of the central Coulomb potential in the medium with dielectric permittivity depending on local condensate density. The condensate density profiles and equimolecular radii for stable and critical droplets at different values of the condensate chemical potential have been computed in the cases of an uncharged solid core with the molecular potential, a charged core