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

One bank problem in the federal funds market