The Boy and the Storekeeper

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.