Its really pretty simple. You have a certain amount of money – known as the princple – and interest is calculated at a fixed rate over a fixed period of time (known as the compounding period). The interest payment is then added to the original principle, and this higher amount becomes the _new_ principle for future calculations.
So, in an example. I have $100 in principle that earns 10% interest every month, and it compounds monthly.
In month 0, I have $100 (my original deposit)
At the end of month 1, I get $10 in interest ($100 * 10%) and its added to my original $100, so now I have $110
At the end of month 2, I get $11 in interest ($110 * 10%) and its added to my previous $110, so now I have $121
At the end of month 3, I get $12.10 in interest ($121 * 10%) and it is added to my previous $121, so now I have $133.10
Etc.
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