Where the Learning Rate Settles

A training run uses a decaying learning-rate schedule. After $t$ optimisation steps the learning rate is

$\eta(t) = \frac{0.05t + 8}{2t + 40}$

The rate starts at $0.2$ when $t = 0$ and decreases from there. An engineer wants to know the floor the schedule is settling onto if training is left to run indefinitely.

What is $\lim_{t \to \infty} \eta(t)$?