do we need to memorize this formula…

I don’t know where this is in the curriculum, but I’ve dealt with on the 2/FM actuarial exam. It’s pretty easy to remember if you understand the mathematics behind it.

I usually track such things via the LOSs. CFA uses trigger words like “calculate,” “interpret,” “describe,” etc. If you see the word “calculate” for Macauly Duration, then we will be expected to know it. Sorry, can’t confirm myself, as I don’t have the material in front of me.

The only formula which you need to remember is the one of effective duration. The other one is also derived from it. No need for this.