The translation equation F(x, s+t) = F(F(x,s),t) plays an important role both in the study of financial laws and the characterization of production functions when the composition of temporal intervals is additive. In order to consider accumulation laws such that the composition of temporal intervals is nonlinear, but just associative, because of uncertainty issues, a generalization of the translation equation can be considered. To this aim a general solution of the functional equation F(x, s <o> t) = F(F(x,s),t), where <o> is the associative operation, is here found. Some properties of the capitalization laws that fulfil the equation are exhibited.
