Formula to figure the final amount received at the end of 1 month that results from starting at 1 cent today which is doubled each day for 1 month assume to be 30 days

Day 1 = 1 cent, day 2 = 2 cents, day 3 = 4 cents etc. Note that on day n the amount received is 2^(n-1). Hence on day 30 you receive 2^29 cents.

To extend this a bit - if you want o add up the total amounts received for the whole month, note that the sum of 1 + 2 + 4 +... +2^(k) = 2^(k+1)-1. So the month-to-date total received is:

Day 1: 2^1-1 = 1
Day 2: 2^2-1 =3
Day 3: 2^3 - 1 = 7
etc.

For a 30 day month the total received works out to 2^30 -1 cents, $10,737,418.23