I am trying to solve the following problem:
Shareholders A and B each have 1/2 of 100,000. This 100,000 is subject to a compounded interest of 5%. Shareholder A however decides to withdraw his share of returns up until a threshold of 50,000 after which he stops withdrawing.
This naturally means that A’s share of the overall value after n periods diminishes until the point where he no longer withdraws. Opposite of course for B.
How does one calculate the total value and each shareholders share after n periods?
A = P(1+r/n)^nt would presumably serve as the base of an answer but as may be evident I am a novice when it comes to anything but rather basic math.
If I understand you correctly A is spending the interest and keeping the principle, while B also keeps the interest untouched.
Therefore the total sum both of them own after n periods is:
$$50000+1,05^n 500000$$
and the share of B of this sum will be:
$$\frac{1,05^n 500000}{50000+1,05^n 500000}$$