What is the derivation for the error due to opamp open loop gain in this case?
But I cannot derive myself why neither I can find a source in internet
  for derivation of this.


Consider this: -



At the point marked with the red X we can say: -

$$(V_{IN}-V_{OUT})\cdot A_{OL} = V_{OUT}$$

$$A_{OL}\cdot V_{IN} = V_{OUT}\cdot(1 + A_{OL})$$

$$\dfrac{V_{OUT}}{V_{IN}} = \dfrac{A_{OL}}{1+A_{OL}}$$

Can you take it from here and plug some numbers in?