I have $2000$ dollars, and I lost $20$% of it in the first month of investment.
In the second month, I got $20$% increase on the value I had left from the loss of the past month.
So, I had $2000$ dollars at first and lost $20$%. So I had $1600$ dollars left.
In the next month, those $1600$ dollars had a $20$% return and then I have $1920$ dollars.
I lost $4$% of my original investment in two months.
Having only the percentage gain and increase, how do you find the $4$% without making calculations with the original value?
Say I have $20$% loss in the first month, then $20$% gain of the remaining value. How do I use those two percentages to find that $4$%?
We have \begin{align} x_0 &= 2000 \\ x_1 &= x_0 (1 - p_1) \quad p_1 = 20\% = 20 / 100 = 0.2 \\ x_2 &= x_1 (1 + p_2) \quad p_2 = p_1 \\ \end{align} where $x_i$ is the money amount after $i$ months passed.
We can combine the last two equations into $$ x_2 = x_0 (1 - p_1)(1+ p_1) = x_0 (1 - p_1^2) = x_0 (1-0.04) $$ which means a decrease of $4\%$ from $x_0$ to $x_2$.