Let's say you have initial seed money x. You would like to compound your trade profit so it will be used up 100% at a time.
The exchange has a fee (f) of 0.1% per trade based on the trade size which is seed money (x) divided by close price (c). Lets say crypto, cry, price is $20.
Then the account balance after the first trade is (seed/close - fee) or
$$\frac{x}{c} - \frac{x}{c} * f = \frac{100}{20} - (\frac{100}{20}*0.001) = 5 - 0.005= 4.995 cry$$
Let's say then you do 10 trades in which you make money or the close price of the exit is bigger than the close price of the entry. (And you're compounding the trade and the profits. So you use 100% of the account balance available after each trade)
What will be a formula for find that? Is it just $\frac{x}{c} - \frac{x}{c} * f $ at each step or trade? The account balance will grow and the fees will also increase in amount but not in percentages
You need to specify a process for the closing prices. Your initial calculation is right, after the first transaction you have (letting $c_0$ be the closing price on the first day)
$$ \frac{x}{c_0}(1-f)$$
If the next day you convert back to \$ amounts at closing price $c_1$ and pay again the fee, you'll have
$$ \frac{x}{c_0}c_1(1-f)^2$$
and so forth.