## Monday, September 18, 2006

### 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.

denise said...

I used this with my jr. high students last December. When Grandpa asks you what you want for Christmas, just say, "Only a few pennies..."

Praveen said...

Hi Denise,

It's amazing, isn't it...

I like your blog, by the way. I think more children (and adults) would appreciate math if they see it as fun, and a tool to solving problems, rather than an isolated activity.

Praveen