Cloak catch up

I saw that they just added a catch up mechanic and was thinking about coming back. My cloak is level 4 right now. How long would it take me to get to a point where I wouldn’t have to worry about it?

Level 15 is the max, I think. Everyday it changes), and at level 9, you need 6 books. I am at level 9 on one of my characters.

How long does it take to get each level?

I think as of this past Tuesday, it takes only one book to increase your cloak. I may of read it wrong. But with that, the ranks also increased essence wise.