The model of this paper gives a convenient strategy that a bank in the
federal funds market can use in order to maximize its profit in a
contemporaneous reserve requirement (CRR) regime. The reserve requirements are
determined by the demand deposit process, modelled as a Brownian motion with
drift. We propose a new model in which the cumulative funds purchases and sales
are discounted at possible different rates. We formulate and solve the problem
of finding the bank's optimal strategy. The model can be extended to involve
the bank's asset size and we obtain that, under some conditions, the optimal
upper barrier for fund sales is a linear function of the asset size. As a
consequence, the bank net purchase amount is linear in the asset size.