Cellular Internet of Things (CIoT) is a Low-Power Wide-Area Network (LPWAN) technology. It aims for cheap, low-complexity IoT devices that enable large-scale deployments and wide-area coverage. Moreover, to make large-scale deployments of CIoT devices in remote and hard-to-access locations possible, a long device battery life is one of the main objectives of these devices. To this end, 3GPP has defined several energy-saving mechanisms for CIoT technologies, not least for the Narrow-Band Internet of Things~(NB-IoT) technology, one of the major CIoT technologies. Examples of mechanisms defined include CONNECTED-mode DRX (cDRX), Release Assistance Indicator (RAI), and Power Saving Mode (PSM). This paper considers the impact of the essential energy-saving mechanisms on minimizing the energy consumption of NB-IoT devices, especially the cDRX and RAI mechanisms. The paper uses a purpose-built NB-IoT simulator that has been tested in terms of its built-in energy-saving mechanisms and validated with real-world NB-IoT measurements. The simulated results show that it is possible to save 70\%-90\% in energy consumption by enabling the cDRX and RAI. In fact, the results suggest that battery life of 10\,years is only achievable provided the cDRX, RAI, and PSM energy-saving mechanisms are correctly configured and used.