Based on FV=C0*(1+r)^n
Where
C0 = Cash flow at the initial point (Present value)
r = Rate of return
n = number of periods
Is there a way to adapt this formula to
(1) In each period, only a% of the interest gained in that period remains in the sum? (in other words: in each period, b% of the interest gained in that period is taken off the sum)
(2) In each period, N (given N is an absolute number) is taken off the sum?
In a real-world scenario, I'm looking for a formula where people will, in every period, take a certain amount (either a % or an absolute value) from the interest of their investment.
For your first question $$ FV = C_0(1+a\times r)^n $$ In this formula I supposed that the percentage remaining ($a$%) is fixed and does not depend on the period.
For your second question $$ ((C_0(1+r)-N)(1+r)-N)\cdots(1-r) - N $$ In this case the formula is trickier and I do not think there is a tidier way to write it. This happens because the interest compounds but the amount taken off is constant. If we have had worked with simple interest (instead of compound interest) then this formula would have been $$ C_0(1+n\times r)-n\times N $$