To a certain extent, people adapt to the adverse consequences of old age as well as to most other undesired events. However, there is evidence to suggest that young people typically underestimate their ability to adapt to it (Lacey, Smith and Ubel, 2006).  The objective of this paper is to study through a simple two period (young/old) model the consequences of this cognitive adaptation to old age and of its misprediction on consumption and leisure. The underestimation of adaptation to old age is modelled as a projection bias in the spirit of in the spirit of Loewenstein, O’Donoghue and Rabin (2003). Under standard and general assumptions, we show that as long as the marginal utility of consumption depends negatively of health, this bias leads individuals to oversave at the expense of their first-period consumption of ordinary goods and leisure. Moreover, there is a substitution between cognitive adaptation and the active strategy of adaptation through saving by which the individual tries to offset the future negative impact of ageing on his well-being by raising his future consumption. We discuss briefly to conclude the possibility that the interplay of both processes of adaptation could help to explain the old age paradox