[Math] Compound interest coumpounded n time per year formula. $A=P\left(1+\frac{r}{n}\right)^{nt}$ intuition behind it.

Question

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?

Answer 1

So the intuition behind it is that compounding interest multiple times in a year is the same as compounding at a rate $\frac{r}{n}$, $n$ times.

So, we have $A=P((1+\frac{r}{n})(1+\frac{r}{n})(1+\frac{r}{n})...(1+\frac{r}{n}))^{t}=P(1+\frac{r}{n})^{nt}$