Find the continous compounding rate if the monthly rate is $12$%

Question

I am clearly missing something here but in the solutions I have that:

$e^r = (1 + \frac{0.12}{12})^{12}$ I am aware of the limit form of $e $ but I don't understand where the above equation came from.

Answer 1

Let monthly rate be $r_m$ so after $1$ year the Interest paid will be $P(1 + \frac {r_m}{12})^{12}$

Let the continual rate be $r$ so after $1$ year the interest paid will be $Pe^r$.

So $e^r = (1 + \frac {r_m}{12})^{12}$.