What is the value of the VAT when you know the percentage and final sum

Question

Assuming we have the final value 444,14. Knowing that this final value includes a 24% VAT, what was the amount of the VAT?

I can figure out the sum before the VAT like this: (444,14 / 124) * 100 = 358,18.

However I have some hard time calculating the actual VAT amount. I know I can do 444,14 - 358,18 = 85,96 but how can I figure out this 85,96 if I know only the final value 444,14 and that includes a 24% value?

Answer 1

Let $final\;value=V$ and $percentage=p\%$

Then $VAT=V-\dfrac{100}{100+p}\,V=V\left(1-\dfrac{100}{100+p}\right)=V\,\dfrac{p}{100+p}$

$$VAT=V\frac{p}{100+p}$$

Hope this helps

Answer 2

Final value = $x$

Sum before VAT = $(x/124*100)=\frac{100}{124}x$

VAT = (final value) - (sum before VAT) = $x-\frac{100}{124}x=\frac{24}{124}x$

Answer 3

If $x$ is the original amount before applying VAT and $A$ is the final amount (in your case $A=444.14$), then $$ A=x+\frac{24}{100}x=\frac{124}{100}x $$ and therefore (with rounding) $$ x=\frac{100}{124}A=\frac{100}{124}\cdot 444.14=358.18 $$ From the first equation you see that the added amount is $$ \frac{24}{100}x=A-x $$ If you want it directly from the final amount, call it $y$. Then $$ y=\frac{24}{100}x=\frac{24}{100}\frac{100}{124}A=\frac{24}{124}A $$ With rounding, $$ \frac{24}{124}\cdot 444.14=85.96 $$