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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.

42piratas
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1 Answers1

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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 $$ C_0(1+n\times r)-n\times N $$

Pekisch
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  • That's super interesting, thanks! I'm trying to subtract a certain percent (b%, given b = 1 - a) of the interest gained in the period only, not taking it from the total amount. – 42piratas Feb 04 '21 at 22:41
  • You mean that you substract only in one period, and leave the rest of the periods with the full interest r? – Pekisch Feb 05 '21 at 00:04
  • No, sorry, I haven't explained well. I mean for every period, I subtract n% of r. So n% of r1, n% of r2,... – 42piratas Feb 05 '21 at 01:06
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    Ok, that formula works that way, it substracts b=1-a% in every period – Pekisch Feb 05 '21 at 01:25