The theoretical and practical understanding of projected changes in rainfall is desirable for planning and adapting to climate change. In this study, finite size Lyapunov exponents (FSLE) are used to study error growth rates of the system at different timescales. This is done to quantify the impact of enhanced anthropogenic greenhouse gas emissions on the predictability of fast and slow varying components of central Indian rainfall (CIR). The CIR time series for this purpose is constructed using the daily gridded high-resolution India Meteorological Department (IMD) dataset and Coupled Model Inter-comparison Project phase 5 (CMIP5) output for historical run and three representative concentration pathways (RCP2.6, RCP4.5, and RCP8.5) from the HadGEM2-ES, IPSL-CM5A-LR, CCSM4, BCC-CSM1.1, and MPI-ESM-LR models. The analyzed CIR dataset reveals a low dimensional chaotic attractor, suggesting that CIR requires a minimum of 5 and maximum of 11 variables to describe the state of the system. FSLE analysis shows a rapid decrease in the Lyapunov exponent with increasing timescales. This analysis suggests a predictability of about 2–3 weeks for fast varying components at short timescale of the CIR and about 5–9 years for slow varying components at long timescales.