What is Compound Interest?

Legal Definition
The addition of interest to the principal sum of a loan or deposit is called compounding. Compound interest is interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously-accumulated interest. Compound interest is standard in finance and economics.

Compound interest may be contrasted with simple interest, where interest is not added to the principal, so there is no compounding. The simple annual interest rate is the interest amount per period, multiplied by the number of periods per year. The simple annual interest rate is also known as the nominal interest rate (not to be confused with nominal as opposed to real interest rates).
-- Wikipedia
Legal Definition
Interest allowed upon interest; for example, when a sum of money due for interest, is added to the principal, and then bears interest. This is not, in general, allowed. See Interest for money.
-- Bouviers Law Dictionary
Legal Definition
is interest upon interest, where accrued interest is added to the principal sum, and the whole treated as a new principal, for the calculation of the interest for the next period.
-- Black's Law Dictionary
Legal Definition
Interest upon interest, i. e., when the interest of a sum of money is added to the principal, and then bears interest, which thus becomes a sort of secondary principal. Camp v. Bates, 11 Conn. 487; Woods v. Rankin, 2 Heisk. (Tenn.) 46; U. S. Mortg. Co. v. Sperry (C. C.) 26 Fed. 730.
-- Black's Law Dictionary
Legal Definition
Interest upon accrued interest added to interest upon the principal sum.
-- Ballentine's Law Dictionary