Unlike prospective time perception paradigms, in which participants are aware that they have to estimate forthcoming time, little is known about retrospective time perception in normal aging and Alzheimer's disease (AD). Our paper addresses this shortcoming by comparing prospective and retrospective time estimation in younger adults, older adults, and AD patients. In four prospective tasks (lasting 30s, 60s, 90s, or 120s) participants were asked to read a series of numbers and to provide a verbal estimation of the reading time. In four other retrospective tasks, they were not informed about time judgment until they were asked to provide a verbal estimation of four elapsed time intervals (lasting 30s, 60s, 90s, or 120s). AD participants gave shorter verbal time estimations than older adults and younger participants did, suggesting that time is perceived to pass quickly in these patients. For all participants, the duration of the retrospective tasks was underestimated as compared to the prospective tasks and both estimations were shorter than the real time interval. Prospective time estimation was further correlated with mental time travel, as measured with the Remember/Know paradigm. Mental time travel was even higher correlated with retrospective time estimation. Our findings shed light on the relationship between time perception and the ability to mentally project oneself into time, two skills contributing to human memory functioning. Finally, time perception deficits, as observed in AD patients, can be interpreted in terms of dramatic changes occurring in frontal lobes and hippocampus.