Let $A(X)$ denote the Waldhausen's algebraic K-theory of a space $X$, and let $n$ be odd.

1. Are the rational homotopy groups of $A(S^n)$ known?

2. Is the group $\pi_{2k}(A(S^n))$ finite for all positive $k\ll n$?

References would be appreciated.

Let $A(X)$ denote the Waldhausen's algebraic K-theory of a space $X$, and let $n$ be odd.

1. Are the rational homotopy groups of $A(S^n)$ known?

2. Is the group $\pi_{2k}(A(S^n))$ finite for all positive $k\ll n$?

A reference (or proof sketch) would be appreciated.

EDIT: I found that the answers are stated (without reference or proof) on page 1 in "Homological stability of diffeomorphism groups" by Alexander Berglund and Ib Madsen, http://arxiv.org/abs/1203.4161. Namely, the answers to both questions is yes.