Issues related to reducing the energy demand of residential buildings are still relevant in the light of the energy transition and ongoing climate change. A single-family house from the early 1990s with a heated area of approximately 177 m2, located in the north-eastern part of Poland, was used as a case study. The article contains the results of nine years of measurements that included energy consumption for heating and domestic hot water preparation. It was estimated that the annual final energy consumption was 128.2 kWh/m2 [462 MJ/m2]. After insulating the building envelope and replacing the windows with triple-glazed ones, this value reduced to 68.2 kWh/m2 [246 MJ/m2]. The measurement results were used to build a statistical model, based on multiple regression, to calculate the energy demand of a similar building to the one analysed in this article in any given location. The article presents the second, more advanced, energy simulations model made in the DesignBuilder environment, which enabled additional analysis of the operation of the heating and ventilation system. The scope of this study also included a multi-variant economic analysis of the building energy renovation, in which the Life Cycle Cost (LCC), Net Present Value (NPV) and Internal Rate of Return (IRR) values were determined.