Let $\mathcal{B}$ be a Banach $k$-algebra. Suppose that there exists a finitely generated $k$-algebra $A$ which is dense in $\mathcal{B}$, then there exists an affinoid algebra $\mathcal{A}$ in which $A$ is a dense $k$-sub-algebra and a homomorphism of Banach $k$-algebras $\mathcal{A}\rightarrow\mathcal{B}$ which extends the identiy homomorphism on $A$.