Feb 2019
2
0
Netherlands
Hi,


Today at work I was trying to understand whether a given amount (revenue) is with or without VAT. (vat is 21%).


Here is the amount with VAT (1980.50)
Here is the amount without VAT (1636.4)


The way I've taught myself to add or subtract a percentage from an amount is to either multiply by 1.21 to add 21% or to multiply by 0.79 to subtract 21%.


Here is what confused me today.
If i do this calculation to add 21% to 1636.4 (1636.4 * 1.21), i get 1980.044 (this is correct)
If i do this calculation to subtract 21% from 1980.5 (1980.5 * 0.79) I get 1564.6 (expected to 1636.4)


Why am I not getting 1636.4 when i subtract 21% from 1980.5?


Also. i was told by my colleague to subtract 21% from 1980.5 I am supposed to divide by 1.21. This way the
calculation makes sense (1980.5 / 1.21 = 1636.77).


Why my colleague's way works and why mine does not?


Thanks in advance for your help!
 
Dec 2014
166
126
USA
Here is the amount with VAT (1980.50)
Here is the amount without VAT (1636.4)
If $A$ is the amount w/o VAT, then $A(1.21) = \text{ the amount with VAT}$

since $A(1.21) = \text{ amount with VAT}$, then $A = \dfrac{\text{amount with VAT}}{1.21}$
 
Feb 2019
2
0
Netherlands
If $A$ is the amount w/o VAT, then $A(1.21) = \text{ the amount with VAT}$

since $A(1.21) = \text{ amount with VAT}$, then $A = \dfrac{\text{amount with VAT}}{1.21}$
Thank you for trying to help me with my poor math skills.

What you said is the correct way to calculate an amount with/without VAT. What i want to know is how and why the formula works (specifically for calculating an amount without VAT)? If VAT is 21%, then why not just the amount with VAT * 0.79 to subtract 21%? I dont want to just remember a formula without understanding how it works.
 
Last edited:
Dec 2014
166
126
USA
It's a common misconception that a fixed percentage increase followed by the same percentage decrease gets one back to the original value.

To make things simple, consider the original amount to be 100. A 21% increase of the value 100 would yield the value 121 … ok with that?

Following that increase with a 21% decrease on the new value of 121 will not yield the original value of 100.

The reasoning is that the follow on decrease of 21% is based on the already increased value of 121, not 100. 21% of 121 is 25.41

(.79)(121) = 95.59 = 121 - 25.41

In plain language, 21% of 121 is greater than 21% of 100, hence the decrease is greater than the initial increase.

Hope this clears it up for you.