algebra precalculus - Compound interest coumpounded n time per year formula. $A=Pleft(1+frac{r}{n}right)^{nt}$ intuition behind it.

I know that the compound interest formula for the interest compounded annually is given by $$A=P(1+r)^t$$
I know the intuition behind it. But why the compound interest formula for the interest compounded n time per year is: $$A=P\left(1+\frac{r}{n}\right)^{nt}$$
What's the intuition behind it and why is it true?