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Context. ESA's PLATO space mission, to be launched by the end of 2026, aims to detect and characterise Earth-like planets in their habitable zone using asteroseismology and the analysis of the transit events. The preparation of science objectives will require the implementation of hare-and-hound exercises relying on the massive generation of representative simulated light-curves. Aims. We developed a light-curve simulator named the PLATO Solar-like Light-curve Simulator (PSLS) in order to generate light-curves representative of typical PLATO targets, that is showing simultaneously solar-like oscillations, stellar granulation, and magnetic activity. At the same time, PSLS also aims at mimicking in a realistic way the random noise and the systematic errors representative of the PLATO multi-telescope concept. Methods. To quantify the instrumental systematic errors, we performed a series of simulations at pixel level that include various relevant sources of perturbations expected for PLATO. From the simulated pixels, we extract the photometry as planned on-board and also simulate the quasi-regular updates of the aperture masks during the observations. The simulated light-curves are then corrected for instrumental effects using the instrument point spread functions reconstructed on the basis of a microscanning technique that will be operated during the in-flight calibration phases of the mission. These corrected and simulated light-curves are then fitted by a parametric model, which we incorporated in PSLS. Simulation of the oscillations and granulation signals rely on current state-of-the-art stellar seismology. Results. We show that the instrumental systematic errors dominate the signal only at frequencies below ∼20 μHz. The systematic errors level is found to mainly depend on stellar magnitude and on the detector charge transfer inefficiency. To illustrate how realistic our simulator is, we compared its predictions with observations made by Kepler on three typical targets and found a good qualitative agreement with the observations. Conclusions. PSLS reproduces the main properties of expected PLATO light-curves. Its speed of execution and its inclusion of relevant stellar signals as well as sources of noises representative of the PLATO cameras make it an indispensable tool for the scientific preparation of the PLATO mission. [ABSTRACT FROM AUTHOR]