Compound Interest...what is it and why should we care?

As a broke college student, things like compound interest and retirement funds sound completely irrelevant to anything I need to deal with.  However, when I started researching all the parts of compound interest (which I have to define for class), I realized it's a lot more important than I thought.

I had to do research for this one, even though the idea is simple.  Apparently, if you have a life savings, you receive interest on that amount in a certain period.  After that period is over, another amount of interest gets computed based on the amount you have plus the interest that you received.  At least, that's what I got out of it.  

After a long period of time, that interest builds up, which is something wealthy people have learned to recognize.  If you start when you're young, as the years go by, the amount in your account will accrue almost exponentially.  

For example, if you start out with $1000 in the bank account, 4% interest would give you $40 extra.  The next year, instead of figuring out the interest based on the beginning principle, it will be figured out based on the principle plus the 40 dollars.  That would give you $1081.60 for the second year.  After three years, you should come to $1124.86.  

Taken from Newsweek.