  We prove that any subcritical solution to the Becker-D\"{o}ring equations
converges exponentially fast to the unique steady state with same mass. Our
convergence result is quantitative and we show that the rate of exponential
decay is governed by the spectral gap for the linearized equation, for which
several bounds are provided. This improves the known convergence result by
Jabin & Niethammer (see ref. [14]). Our approach is based on a careful spectral
analysis of the linearized Becker-D\"oring equation (which is new to our
knowledge) in both a Hilbert setting and in certain weighted $\ell^1$ spaces.
This spectral analysis is then combined with uniform exponential moment bounds
of solutions in order to obtain a convergence result for the nonlinear
equation.
