Huh, thanks for the correction.
Smaller correction—I think you’ve had her buy an extra pair of boots. At $260 she’s already bought one pair, so we apply thirteen times, then multiply by 1.07 again for the final year’s interest, and she ends with no boots, so that’s $239.41. (Or start with $280 and apply fourteen times.)
Not sure why my own result is wrong. Part of it is that I forgot to subtract the money actually spent on boots—I did “the $20 she spends after the first year gets one year’s interest, so that’s $21.40; the $20 she spends after the second year gets two years’ interest, so that’s $22.90...” but actually it’s only $1.40, $2.90 and so on. But even accounting for that, I get $222.58. So let’s see...
Suppose she only needs to buy two pairs of boots. According to your method she goes $40 → $21.40 → $1.50. (Or, $40 and no boots → $20 and boots → $21.40 and no boots a year later → $1.40 and boots → $1.50 and no boots a year later.) According to mine, of her original $40, $20 of it earns no interest and $20 of it earns a years’ interest. But that assumes the interest she earns in that year is withdrawn, she gets to keep it but it doesn’t keep earning interest. So that’s why I got the wrong answer.
This seems true and important to me. But also… some people really are incompetent or malicious. A blameless postmortem of the XZ backdoor would miss important parts of that story. A blameless postmortem of Royal Air Maroc Express flight 439 would presumably have left that captain still flying? At any rate, as long as “the captain gets fired” is a possible outcome of the postmortem, the captain has incentive to obfuscate. (Which he tried unsuccessfully. Apparently we don’t know if he was actually fired though.)
I guess there are cases where “ability to get rid of people” is more important than “risk that people successfully obfuscate important details”, and some cases where it’s not. I don’t know how to navigate these.