We present a new method for interpolation in satisfiability modulo theories (SMT) that is aimed at applications in model-checking and invariant inference. The new method allows us to control the finite-convergence of interpolant sequences and, at the same time, provides expressive invariant-driven interpolants. It is based on a novel integration of model-driven quantifier elimination and abstract interpretation into existing SMT frameworks for interpolation. We have integrated the new approach into the Sally model checker and we include experimental evaluation showing its effectiveness.