If nailah gives BayBay 1 penny on day 1 then 2 on day 2 then doubled each sum for a a yr. How much money would BayBay have saved at the end of the year?

That would be 2^365

which is a number so huge that it is unimaginable.
It has been estimated that the total number of atoms in the entire universe is 10^80

We can compare 10^80 with 2^365 by breaking down 2^365 into 2^300 x 2^65
= 2.037 x 10^90 x 3.6893 x 10^19
= 7.515 x 10^109

so your amount of money would be more than all the atoms in the entire universe.

I have seen this question where you find the amount at the end of 1 month, but not a whole year.