Why is it easier to piece a paper with a sharp pin?

Why is it easier to piece a paper with a sharp pin?

We know, if F force is applied to area A perpendicularly, Pressure P = F ፥ A

From this equation, as the area decreases, pressure increases.

The head of the pin is very small and sharp, hence the area is very less. Thus, by applying small force, large pressure can be created. 

That's why it is easier to pierce a paper with a sharp pin.