# 77 transactions to $0 Given variable rate and flat fee structure enforced by payment processing providers like Stripe, how many transactions does it take for $100 to disappear from a local communities economy? This calculation is part of [[My approach to money|my broader approach to money]]. # Solving the math ## Recurrence (per transaction) Let: - `p` = percentage fee (decimal) - `f` = fixed fee (dollars) - `x0` = starting amount (dollars) **Update rule:** $ x_{n+1} = (1-p)x_n - f $ --- ## Closed form (after n transactions) $ x_n = (1-p)^n\left(x_0+\frac{f}{p}\right) - \frac{f}{p} $ --- ## Solve for when the balance drops below a threshold T We want the smallest integer `n` such that: $ x_n < T $ Algebra gives: $ n > \frac{\ln\!\left(\frac{T+\frac{f}{p}}{x_0+\frac{f}{p}}\right)}{\ln(1-p)} $ So: $ n_{\min} = \left\lceil \frac{\ln\!\left(\frac{T+\frac{f}{p}}{x_0+\frac{f}{p}}\right)}{\ln(1-p)} \right\rceil $ --- ## Example (Stripe standard: 2.9% + $0.30) Use: - `p = 0.029` - `f = 0.30` - `x0 = 100` - threshold `T = 1` Compute: $ n_{\min}=\left\lceil \frac{\ln\!\left(\frac{1+\frac{0.30}{0.029}}{100+\frac{0.30}{0.029}}\right)}{\ln(1-0.029)} \right\rceil = \left\lceil \frac{\ln\!\left(\frac{1+10.3448276}{100+10.3448276}\right)}{\ln(0.971)} \right\rceil = \left\lceil \frac{\ln(0.102823)}{\ln(0.971)} \right\rceil = \left\lceil 77.2 \right\rceil = 78 $ **Result:** after **78** transactions, the remaining amount is **< $1**. # What this means What this means is that $100 circulating a local economy via credit cards will exponentially evaporate towards $0. How quickly? The math above shows that After 78 transactions, 99% of the original one hundred dollars will have left the community, being vacuumed up into the coffers of extractive corporations like Paypal, Stripe, Square, and so on.[^1] # What to do about it **As a business** As a business, there's only so much we can do about it. Customers are accustomed to and expect the ease of using their credit card. The best thing to do to educate your customers. Some businesses decide to pass the processing fees on to their customers. Some will simply let them know what's happening and suggest better alternatives. I do both at different times. **As a consumer** Use cash for local businesses. Save your desire to earn credit card points from any spending you *have to do* through corporations like Walmart, Homedepot, or [any of these ones](https://www.ethicalconsumer.org/ethicalcampaigns/boycotts) (all under boycott by Ethical Consumer as of January 2026).