Compounding interest builds on itself
There are two general types of interest rates: simple interest rates and compounding interest rates. Simple interest charges interest only based on principle value; if you lent a friend $100 at a 5% a year rate on simple interest, he'd owe you $5 for each year before he pays you back. Compounding interest charges interest on the principle value, as well as the value of any interest previously accrued. In the same scenario, if you decided to charge your friend a 5% yearly compounding rate, he'd owe you $5 after the first year, then 5% of $105 the second year, and so on. The end result is that your friend would owe you increasingly more under compounding interest the longer it took for him to pay you back.
Compounding interest is the norm in economics and finance
When thinking about money, compounding interest is a much more useful value than simple interest, and as such is used almost exclusively when thinking about interest rates in economics and finance. Money is generally thought to have a compounding value over time, meaning a certain amount of money today, is worth more in the future due to the interest it could generate if lent. Almost all long term investments and savings accounts are calculated using compound interest.
Compounding is the key to savings growth
For investors and savers looking to grow wealth over a long period of time, compounding is a powerful tool that results in exponential gains. This is true due to the fact that over a long enough span of time, the interest gained on savings will eventually be larger than principle, so the interest starts to build more quickly on itself than money you actually put in. For example, $1000 saved at compounding interest that appreciates at 7% each year would be worth 1,967.15 after ten years, 3,869.68 after twenty years and 7,612.26 after thirty. The investment essentially double every ten years, as opposed to a non-compounding rate that would take almost the whole thirty years at 7% to double once.