This work deals with the application of a solvable model to study the accuracy of a nuclear many-body approximation method. Using a new exactly solvable model, we carry out here a quantitative test of the accuracy of the time-dependent Hartree-Fock (TDHF) method. The application of the TDHF method to the model reveals that the model is suitable for describing various forms of collective motion: harmonic and anharmonic oscillations as well as rotations. We then show that, by properly quantizing the TDHF results, the TDHF approximation method yields energy spectra that are in very good agreement with their exact counterparts. This work shows that the model offers a rich and comprehensive framework for studying the various aspects of the TDHF method and also for assessing quantitatively its accuracy.