Let's use an example. If you put $100 into a shoe box on January 1st of every year, at the end of 20 years you would have 20 x $100 = $2,000.
But if you deposit that same $100 into the bank every year and the bank pays you 5% on that deposit at the end of the year, you would earn $5 in interest at the end of the first year and have a total of $105. The calculation is simply 1.05 x $100 = $105
But then the magic happens in the second year. On January 1st of the second year, you now have $105 from the last year plus $100 that you just deposited. The total comes to $205. At the end of the 2nd year the bank adds 5% to your bank account by multiplying 1.05 x $205 = $215.25
Each year for 20 years, you keep depositing $100 on the 1st of the year and the bank adds 5% interest at the end of the year. Here's how much you would save and earn each year:
Through the mathematical magic of compounding interest, you've earned $1,472 more than if you just saved $2,000 in your shoe box!