Compound interest is interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. The effect of compound interest depends on frequency.
Assume an annual interest rate of 12%. If we start the year with $100 and compound only once, at the end of the year, the principal grows to $112 ($100 x 1.12 = $112). If we instead compound each month at 1%, we end up with more than $112 at the end of the year. That is, $100 x 1.01^12 at $112.68. (It's higher because we compounded more frequently.)
Continuously compounded returns compound the most frequently of all. Continuous compounding is the mathematical limit that compound interest can reach. It is an extreme case of compounding since most interest is compounded on a monthly, quarterly or semiannual basis.
Read on to learn how continuously compounded interest is calculated and why it is commonly used in finance.
Source : Investopedia