We consider the supersymmetric model obtained from the Wess-Zumino model with interaction, with the help of a dimensional reduction. The solution is found of the corresponding classical problem with a precision up to terms of the third order of smallness. A quantum model of such a system is constructed. Its spectrum is found in the first and second order of perturbation theory. The supersymmetric finite-dimensional model under consideration proves to be extremely close to the usual anharmonic oscillator.