If I say I will give you a penny on the first day, 2 pennies on the second day, 4 pennies on the third day, and I just keep doubling and do this for a month, How much money would you have at the end of the month???

Over 10 million

sum = 1+2+4+8+16+ ...

= 2^0 + 2^1 + 2^2 + 2^3 + ... 2^30

this is a geometric series
= a(r^n - 1)/(r-1)
= 2(2^30 - 1)/(2-1)
= 2 147 483 646 pennies
= $ 21 474 836.46

(check my arithmetic)

10 dollars

To calculate the amount of money you would have at the end of the month, we need to determine the total number of pennies you receive each day and then convert it to the desired currency.

In this scenario, you start with 1 penny on the first day, and for each subsequent day, the amount doubles. So, on the second day, you would have 2 pennies, on the third day 4 pennies, and so on, doubling each day for a month.

To calculate the total amount of money for each day, you can use the formula:

amount = 2^(day-1)

Now, let's calculate the total amount for each day in pennies for a month:

Day 1: 2^(1-1) = 1 penny
Day 2: 2^(2-1) = 2 pennies
Day 3: 2^(3-1) = 4 pennies
Day 4: 2^(4-1) = 8 pennies
...
Day 30: 2^(30-1) = 536,870,912 pennies

To convert this amount into a more tangible number, we need to divide it by 100 to get the dollar amount, since there are 100 pennies in a dollar:

Day 30: 536,870,912 / 100 = $5,368,709.12

So, at the end of the month, you would have $5,368,709.12.