Use case is for tax calculation.
Tax is at 8.875%. Using $100 tax-inclusive amount, I get different tax amounts using these formulas:
First:
$$\mathrm{taxAmount} = \$100\times 0.08875 = \$8.875$$
Second:
$$\mathrm{taxAmount} = \$100 – (\frac{\$100}{1.08875}) = \$8.15$$
I find the first formula is the correct one and straightforward but a colleague suggests to use the second.
What's the difference and which one is correct?
Best Answer
The first formula is what you should use if $\$100$ is the price before tax, and you are calculating how much tax you need to add on. Thus you have prices of $\$100$ (net) and $\$108.875$ (gross, i.e. net plus tax).
The second formula is what you should use if $\$100$ is the price after tax, and you want to work out how much of this was tax. So here you have prices of $\$100$ (gross) and $\$91.85$ (net, i.e. gross minus tax).
As a check, if you apply the first formula to a net price of $\$91.85$ you should get back to $\$100$ gross (there is a small error because the $\$8.15$ in your post is rounded to the nearest cent).