We propose a model of inter-bank lending and borrowing. The evolution of log- monetary reserves of N banks is described by coupled diffusions driven by controls in their drifts. Banks are minimizing their finite-horizon objective functions which take into account a quadratic cost for lending or borrowing and a linear incentive to borrow if the reserve is low or lend if the reserve is high relative to the average capitalization of the system. We solve the open-loop equilibrium through the forward and backward stochastic differential equations. In addition, we apply the coupled Hamilton-Jacobi- Bellman equations to obtain the closed-loop equilibrium under Markovian setting. Finally, mean field games in the form of N going to infinity are discussed.