I remember my mom calling it the “miracle of compound interest.” I was 14 or something at the time, and when she tapped out on her calculator with the ribbon of paper coming out the top showing me how to get free money, I was in awe! A miracle, magic, basic accounting, whatever you want to call it, it's great. So what is it?
Basically, it's earning #interest on interest. Each time that interest is calculated on the amount you have saved, it includes the interest that you earned last time. So if you start with $100 and get 2% interest per year (and don't add any more money), you'll have $102 at the end of year. Next year that 2% is calculated using $102, so you'll have $104.04. I could have left off the 4 cents for a nice round number, but hey, that's 4 cents of money I won't deprive you of. You worked hard for it. But wait, you didn't. That's the best part! You didn't do a thing for it other than let someone hold on to your money. At the end of the 10 years you'd have $121.90. Again, it's free money people.
Most banks actually give you the interest monthly instead of yearly. Just take the interest rate and divide by 12 months to get the monthly percent. So each month you'd get .00167% or 16 cents on that $100. At the end of one year you'd have $102.02, and after 10 years $122.12. Remember the assumption was that you started with $100 and then did absolutely nothing but forget about your money. If instead you kept up with saving and put in $100 every month you'd end the year with $1,213.08. Now we're getting somewhere.
For those who like to see it laid out simply:
Simple interest: Original $ Amount x Interest rate x Length of Time (in years) = Amount Earned
Compound interest: (Original $ Amount + Earned Interest) x Interest Rate x Length of Time = Amount Earned
If all of this is just a bit too UGH, don't stress out. I'm here for you.