  The exact entropy of two-charge supersymmetric black holes in N=4 string
theories is computed to all orders using Wald's formula and the supersymmetric
attractor equations with an effective action that includes the relevant higher
curvature terms. Classically, these black holes have zero area but the
attractor equations are still applicable at the quantum level. The quantum
corrected macroscopic entropy agrees precisely with the microscopic counting
for an infinite tower of fundamental string states to all orders in an
asymptotic expansion.
