Free subalgebras of graded algebras

Let k be a field and let A=⨁n≥1An be a positively graded k-algebra. We recall that A is graded nilpotent if for every d≥1, the subalgebra of A generated by elements of degree d is nilpotent. We give a method of producing grading nilpotent algebras and use this to prove that over any base field k there exists a finitely generated graded nilpotent algebra that contains a free k-subalgebra on two generators.