How to calculate compound interest percentage from one period to another? For example, if I have a compound interest percentage of $30\%$ for a month, how can I translate this percentage for the period of a day?
I guess $30\% / 30$ (nb of days) $= 1\%$ is not the correct answer.
Best regards
N.B: I am also interested to know for the reverse situation, i.e from a small period to a larger one.

The daily rate ($r_d$) relates to the monthly rate ($r_m$) through the relation
$$(1+r_d)^{30} = 1 + r_m$$
If you solve with respect to $r_d$, you get
$$r_d = (1+r_m)^{1/30} - 1.$$
In your specific case, $r_d = 0.00878383 \approx 0.878\%$. The reverse situation works in the same way, you use the first equation and solve it with respect to $r_m$, i.e.
$$r_m = (1+r_d)^{30}-1.$$
