Deriving APY from starting and ending balance

Question

Suppose I have a starting balance of 3000 USD and at the end of the month I have a final balance of 3600 USD.

How would I calculate what the APY is based on just the starting and ending balance?

Answer 1

I should have been clearer and added more calculations sorry.

You have a $20$% rate since $\Big(\frac{3600-3000}{3000} \times 100 = 20 \Big)$ hence, $$APY = \Big(1 + \frac{0.2}{12} \Big)^{12} - 1. $$ By the formula $APY = \Big( 1 + \frac{r}{n}\Big)^n - 1$, where $r = 0.2$ and $n = 12$ since it is being compounded monthly. Therefore by the above calculation you should have an APY of $0.21939...$ i.e. $21.93$%.