The voluntary investment of mental effort is an understudied aspect of cognitive control, whose underlying mechanisms remain poorly understood. Here, we investigated this process using a computational model of the Stroop task within the framework of active inference. In the Stroop task, participants must report the font color of a presented color name, while suppressing the automatic tendency to read the word itself. In this study, we asked twenty healthy young adults to perform the Stroop task under two conditions: with maximum exertion or as relaxed as possible. Their behavior was modeled using a two-layer generative model grounded in active inference, conceptualizing cognitive effort as the extent to which habitual response tendencies are overridden by goal-directed behavior. This approach enabled the estimation of two key latent parameters: (i) the individual's habitual bias toward word reading over color naming and (ii) the degree of motivation to perform the task correctly. Our findings indicate that voluntary engagement of maximal effort was associated with an increased preference for correct performance, whereas its relationship with the habitual bias toward word reading did not show a consistent group effect. These results support the hypothesis that the voluntary investment of cognitive effort is primarily governed by an increased motivation for accuracy rather than by the direct inhibition of habitual response tendencies. This computational approach holds potential relevance for clinical settings where impaired intentional effort allocation is observed in psychiatric and neurological disorders.