The present worth (PW) and future worth (FW) decision criteria are to be found in virtually all current engineering economy textbooks. Although the relationships between the internal rate of return (IRR) criterion and PW has been widely discussed in the literature, there remains some misunderstanding as to similar relationships between PW and FW. Of particular importance is the interest rates at which PW and FW are maximized. It is shown here that the maximizing rates are not necessarily equal. This leads to the seemingly peculiar result that a change in the discount rate may decrease the PW while at the same time increasing the FW, or vice versa. Numerical, mathematical and intuitive arguments are presented.