Age-period-cohort models provide a useful method for modeling incidence and mortality rates. There is great interest in estimating the rates of disease at given future time-points in order that plans can be made for the provision of the required future services. In the setting of using age-period-cohort models incorporating restricted cubic splines, a new technique for projecting incidence is proposed. The new technique projects the period and cohort terms linearly from 10 years within the range of the available data in order to give projections that are based on recent trends. The method is validated via a comparison with existing methods in the setting of Finnish cancer registry data. The reasons for the improvements seen for the newly proposed method are twofold. Firstly, improvements are seen due to the finer splitting of the timescale to give a more continuous estimate of the incidence rate. Secondly, the new method uses more recent trends to dictate the future projections than previously proposed methods.