While I am skeptical that it's the case, you seem to have missed the assertion that r < 0. In that case, the "shrinking" of the wealth gap by 1/(1+r) would be

While I am skeptical that it's the case, you seem to have missed the assertion that r < 0. In that case, the "shrinking" of the wealth gap by 1/(1+r) would be more accurately termed a growing by 1/(1-r).