The behavior of retired lithium-ion battery (LIB) from its first-life application such as electric vehicles and electric aircraft for its second-life in a solar photovoltaic (PV) grid-tied system for residential applications is studied through mathematical modeling. The rate of capacity-fade and the useful remaining life of the retired- or used-LIB particularly investigated in this paper. The first part of this paper presents the optimal size of a small-scale battery energy storage system (BESS) to store a part of the solar energy for postponing consumption in the near future for a typical home in Akron, Ohio. The LIBs in this study has lithium nickel manganese cobalt oxide (NMC) chemistry. The sizing is determined based on a set of PV panels, power rate of the BESS, and hourly data of temperatures, irradiation and home demand load. Using PVWatts® Calculator from National Renewable Energy Laboratory (NREL), the hourly PV performance data of the PV generation system is obtained. In this study, the home is connected to the grid, but the net energy usage from the grid in one year is zero. The duty-cycle of the PV generation is obtained in order to design a LIB energy storage system using calculations of the PV system hourly energy production. The difference between the residential home demand and PV generation is used to evaluate the excess energy that charges the battery and is sold to the electric grid. In the second part, the retired- or the used-battery degradation rate and its remaining useful second-life in the BESS are estimated using an empirical battery model. This model includes the capacity-fade of the LIB for both first- and second-life applications under different operating and environmental conditions. It is shown that a used-LIB from first-life applications is still suitable to be used for this system. The results show that the investigated used-LIB is capable of being in-service for another 10 years in the PV system for residential application. The results of this paper can potentially reduce the battery cost for electric vehicles and electric aircraft because the retired battery from these applications have still value to serve for another applications such as PV system for residential homes. Since this study is based on mathematical modeling, several assumptions have been made in the model. Although the results of mathematical modeling is very promising, these results should be proved experimentally. The experimental studies is out of the scope of this paper.