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The recurrence and timing
Each month begins with the previous ending members. The model removes the stated fraction of beginning members, then adds new paid joins at period end: M[t+1] = M[t] × (1 − c) + J. Realized price times the ending member count gives an ending monthly revenue run rate.
Run rate is not actual total period cash or recognized revenue. Join and billing dates, refunds, taxes, payment failures and plan migration can change the relationship. The optional variable-cost line is only the cost you enter; it is not net profit.
Independent example
Starting with 1,000 members, 4% attrition, no joins and twelve months produces 612.7098 modeled members. At $30 per month, the ending monthly run rate is $18,381.29. With 40 paid joins at each month-end, the recurrence stays at 1,000. Zero attrition and no joins leave the cohort unchanged.
Use the result to ask a better question
A model does not prove that a site’s input is sustainable. Compare canceled beginning members with new joins, reconcile successful collections and separate free/paused accounts. Read the membership diligence guide before treating a dashboard count as reliable recurring revenue.
Translate account and visit assumptions into contribution
Use the retail and membership break-even tool to separate paid-account revenue, included-visit costs and retail wash contribution. Required volume is a scenario, not proof of demand.