Why do gym visits spike right after a prepaid annual membership is bought, then fade away by the tenth month?

Answer: The sting of paying is vivid at first and then fades over the months.

The early visits come from a gym habit that builds steadily and then persists all year. — Not quite. Habits do get stronger with repetition, and a run of early visits can genuinely help build one, so this captures something real. But a habit that keeps building would predict steady or rising attendance later in the year, not a slide by month ten. What separates the first week from the fortieth is how fresh the payment feels, not how settled the routine is.

The longer the unused membership sits, the more the wasted money gnaws at people. — Not quite. Disliking waste is real, and it is part of why the member goes at all. The mistake is the direction: if unused money nagged harder the longer it sat there, attendance would climb through the year instead of sagging. The opposite happens, because the pull of an old payment weakens even while the unused membership still has value.

The sting of paying is vivid at first and then fades over the months. ✓ — Right. Payment-depreciation research finds that when a cost is separated in time from what it buys, its power to push behavior decays, which fits the early spike and the later fade. Nothing about the membership itself changed; only how loudly that old payment speaks changed. That is why prepaying can drive people to the gym early in the year without carrying them through month ten.