Whilst a net zero energy (NZE) home produces the same amount of energy as it consumes it still exchanges significant amount of energy with the grid due to mismatch between the generation and load patterns. Consequently, the homeowner has to pay an annual electric bill because the cost of imported energy is usually higher than that of exported energy. Installing a local battery energy storage system (BESS) can reduce the electric bill by exchanging less energy with the grid. This paper proposes a method of determining the optimal size of a BESS for a typical NZE home with rooftop solar photovoltaic (PV) system to minimize the annual net payment for electricity and battery cost. The optimal battery size is determined through solving an optimization problem which is formulated using hourly load and PV generation data for a South Australian home, battery annual payment rate, retail price (RP), and feed-in tariff (FIT). The effects of interest rate, RP and FIT on the annual net payment are investigated. The results obtained are thoroughly analysed and clearly indicate that, with current installation cost of BESS and South Australian RP and FIT, the use of a local BESS is economically beneficial for the homeowner.