Upper bound for exponential random variable

Question

For $N>\mu>0$, I wonder how to show that

$$ \left(1-\frac {\mu}{N}\right)^{N-\mu}\geq e^{-\mu}. $$

The only thing I know is

$$ e^{-\mu}\geq \left(1-\frac {\mu}{N}\right)^{N}. $$

But I don't know how to derive the required inequality from this.