Taxes calculations on goods: there is something I'm missing

Question

Lets say I have a good that costs 1000 Eur including taxes and that the applied tax rate is 22%.

Gross price = 1000 Eur;
Tax rate = 22% = 0.22;

Taxes amount = 1000 * 22% = 220 Eur
Net amount = 1000 - ( 1 * 22% ) = 780 Eur
Taxes amount + Net Amount = 1000

Up to here no problems.

The problem arises if I want to calculate the gross price given the net price (780):

Gross price = 780 + (780*22%) = 951.6

There is something I'm missing: I expect the gross price is again 1000 Eur, while it is of 951.6 Eur. I'm missing 48.40 Eur...

What am I doing wrong? o.O

Answer 1

As the gross price is the net amount multiplied with one plus tax/100, you find the net amount from the gross price by dividing by one plus tax/100

$$ \text{net amount}=\frac{1000}{1+22/100}\approx 819.67$$