How do calculate a fee from a given percentage Scenario:
I want to buy a share in a company.

*

*Cost per share = 50,000USD


*Number of shares to buy = 0.5


*Transaction fees = 0.2%

Calculations:

*

*Convert fee percentage to a decimal : 0.2 / 100 = 0.002


*Convert decimal fee to amount to subtract from shares : 1 - 0.002 = 0.998


*Calculate shares bought after fees : 0.5 * 0.998 = 0.499

Two part question:

*

*Is the calculation correct?

*Is there a better, simpler way of doing this?


Suppose you want to spend $d$ dollars for shares and that amount should include the commission $c$ (expressed as a fraction, not a percent). Let $s$ be the amount that will go to shares. Then
$$
(1+c)s = d
$$
so
$$
s = \frac{d}{1+c}.
$$
That is not the same as what you calculated, which is $s(1-c)$. But when $c$ is very small (as it is in this case) they are very close. You can check the difference numerically.
