verify the calculation of periodicity

Hello everyone,

I would like to confirm the proper computation for periodicity. Upon doing some exercises, I just realized it is through algebra to get the value of APR in the formula of periodicity. I’ve been doing it through calculator by replacing the periods, but I didn’t get the exact answer. How do you do this periodicity?

Thank you so much!

Can you set an example with numbers of what you trying to solve please?