A spectral colour prediction model is proposed and applied to an ink jet printer. We limit the field of investigation to transparent inks printed on a transparent substrate. The proposed method is based on the computation of the transmittance spectra of colour primaries applying Beer's law, and on the calculation of their respective surface coverage using a high resolution grid. The proposed prediction model requires measuring the transmittance spectra of the inks and approximating the density distribution function of a single printed dot of each ink. We hereby obtain accurate spectral predictions of colour patches, while the number of required sample measurements is reduced to a minimum.