A boy went to his neighborhood store and asked to work for 1 month. He offered to work the first day for a penny, as long as it was doubled each day.
The amused shopkeeper agreed, and even signed a contract.
Well, of course, the boy ended up owning the store! The boy's pay on the last day of the month (31th day) was $10,737,418.24!
Such is the power of compounding.
Mathematically, we can describe compounding as multiplying the starting amount by (1 + interest rate/100) raised to the number of time intervals.
For example, $100 compunded at 10%/year for 3 years would be:
100 X 1.10^3
In the boy's case, we would calculate his pay for any given day D as:
0.01 X 2^(D-1)
(We use D-1 because the figure is calculated for the day, not for the end of it).
So, on day 1, the boy gets 0.01 X 2^0 = $0.01.
On day 4, the boy gets 0.01 X 2^3 = $0.08
On day 10, 0.01 X 2^10 = $10.24, and so on.