Buy/Sell

Calculate the selling price to obtain a given gain

@@B@@
@@F@@ %
@@T@@ %
@@G@@ @@S@@ @@S'@@ @@S''@@
% =
Selling price @@S@@ to obtain gains of @@G@@% if there is no selling fees and no gains tax:
@@S - B = \frac{G}{100} B \iff S = B \left(\frac{G}{100} + 1\right)@@
Selling price @@S'@@ to obtain gains of @@G@@% if there is @@F@@% selling fees, but no gains tax:
@@\left(S' \frac{100\,-\,F}{100} - B\right) = \frac{G}{100} B \iff S' = B \frac{100\,+\,G}{100\,-\,F}@@
Selling price @@S''@@ to obtain gains of @@G@@% if there is @@F@@% selling fees and @@T@@% gains tax:
@@\left(S'' \frac{100\,-\,F}{100} - B\right) \frac{100\,-\,T}{100} = \frac{G}{100} B \iff S'' = B \frac{100}{100\,-\,F} \left(\frac{G}{100\,-\,T} + 1\right)@@

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