  We show that the superconformal index of N=1 superconformal field theories in
four dimensions has an asymptotic growth of states which is exponential in the
charges. Our analysis holds in a Cardy-like limit of large charges, for which
the index is dominated by small values of chemical potentials. In this limit we
find the saddle points of the integral that defines the superconformal index
using two different methods. One method, valid for finite N, is to first take
the Cardy-like limit and then find the saddle points. The other method is to
analyze the saddle points at large N and then take the Cardy-like limit. The
result of both analyses is that the asymptotic growth of states of the
superconformal index exactly agrees with the Bekenstein-Hawking entropy of
supersymmetric black holes in the dual AdS$_5$ theory.
