How do calculate a fee from a given percentage

Question

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%

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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

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Two part question:

1. Is the calculation correct?
2. Is there a better, simpler way of doing this?

Answer 1

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.

Answer 2

I could be mistaken, but I don't think transaction fees are calculated in that way. If you buy two shares, spending $\$100,000$ then you will have to pay an additional $\$200$ in transaction fees.

Therefore, the fraction of outlay that goes toward the transaction fee is

$$\frac{200}{100200} ~\text{rather than}~ \frac{200}{100000}.$$

The natural question is, since my proposed interpretation leads to less profit for the bank/brokerage house, why would they accept such an interpretation? Answer : because the math is easier for their bookkeepers to understand.

Actually, I could be mistaken; I simply suspect that my interpretation is how the calculations are actually done.