This is the question that I'm struggling with. Why 0.9 instead of 0.1? And what happens to the M0? These questions might sound stupid but I'm just trying to understand.
10% is just how much of it has decayed. But that’s not gonna help us measure anything easily.
Because how else can we measure what percentage decays in the next year? Or the year after that? (Note that in fact, in the second year what’s decayed is 90% * 10%, i.e. 9%. And in fact, another 8.1% decays in the third year.)
This is because the amount that decays per year is not dependent on how much has decayed last year, but rather how much from last year has
not decayed. The problem is then that to figure out the total decay, we need to keep a running record of how much decays only in the n-th year, and then do the sum of a GP.
It turns out it is much easier to just resort to keeping track of
how much is there still left, as opposed to what’s already decayed. This simplified the computations a lot more.
The M0 simply gets cancelled out on both sides of the equation. We don’t need to know what M0 is to complete the question
Also note that the post had a mistake, which was addressed a bit further down
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