This study investigates (1) the economics of adding a battery to a residential photovoltaic (PV) system and (2) how different home energy management (HEM) strategies impact its profitability in a Finnish context. Our key novelty is the analysis on highly varying dynamic electricity prices from years 2020–2022 accompanied with the calculation of battery usage costs coming from battery degradation. Furthermore, by implementing multiple HEM strategies with variable complexity on real PV production and four real electricity consumption data, we provide a comprehensive study methodology. We tested five strategies, ranging from simple rule-based (SCM) to optimization (MPC) and reinforcement learning (RL) approaches. Our findings indicate that adding a typical 13.5 kWh/9000 EUR battery to a 4 kWp PV system is economically unfeasible for balancing the intermittent PV production under the current electricity prices in Finland. Two of the strategies considered battery usage costs in the decision making, leading to the battery staying unused, due to higher battery usage costs than electricity bill savings. The economic break-even battery capital expenditures (CAPEX) were 185 EUR/kWh at best under the high electricity prices of 2022. This is under a third of the given CAPEX of 667 EUR/kWh. Interestingly, the simple SCM resulted in practically equal electricity bill savings to complex MPC and RL in 2020–2021. However, during the elevated and highly varying prices in 2022, MPC achieved 5.7% lower electricity bills compared with SCM. Thus, complex HEM strategies were beneficial here only during volatile electricity prices.