How to determine the monthly interest rate from an annual interest rate

If the stated annual rate is $2.549\%$, you would divide by $12$ to get the monthly rate.

However, if the effective annual rate is $2.549\%$, then letting the monthly rate be $i$, we have $(1+i)^{12}=1.02549$. So $i=\sqrt[12]{1.02549}-1\approx .0021$, or $0.21\%$

Let's denote by $L$ the value of the loan, $m$ the monthly rate and $a$ the annual rate. $M$ is the total number of months of the debt and $A$ is the total number of year of the debt (of course, $A=12M$).

What you owe from beginning of month $\mathcal{M}$ to end of month $\mathcal{M}$ is: $$(1+m)^\mathcal{M}\times \dfrac{L}{M}$$

For example is the interest is 0, you will owe $L/M$ each month.

Similarly, for what you owe for year $\mathcal{A}$ is: $$(1+a)^\mathcal{A}\times\dfrac{L}{A}$$

Now, let's write that the interest rates $a$ and $m$ are such that and the end of the first year, both values should be equal (12 times what your owe monthly and 1 time what you owe annualy):

$$12\times(1+m)^\mathcal{12}\times \dfrac{L}{12}=(1+a)^1\times\dfrac{L}{1}$$

This gives (almost, you forgot to substract 1) your first formula: $$\boxed{a=(1+m)^{12}-1}$$

To express $m$ as a function of $a$, you just have to manipulate this formula: $$(1+a)^{1/12}=(1+m)^{12/12}$$ so $$\boxed{m=(1+a)^{\frac{1}{12}}-1}$$

With $a=0.02549$, the calculation yields: $0.00210$ so the monthly rate is $0.21\%$, which is not equal to $0.02549/12$, because you pay interest on the interest which has not been refunded yet.