What does "continuous compounding" refer to in finance?

Continuous compounding refers to the process of calculating interest and adding it to the principal amount at every possible moment rather than just at regular intervals, such as annually or semi-annually. This means that interest is not only earned on the initial principal but also on the interest that has already been added to the principal over time.

In financial mathematics, continuous compounding can be expressed using the formula ( A = Pe^{rt} ), where ( A ) is the amount of money accumulated after ( n ) years, including interest, ( P ) is the principal amount, ( r ) is the annual interest rate, ( t ) is the time the money is invested or borrowed for, and ( e ) is Euler's number, approximately equal to 2.71828. This illustrates how continuously compounding interest leads to exponential growth of investments or debt.

In contrast to continuous compounding, other options describe more traditional methods of calculating interest that do not account for the instantaneous addition of interest, such as periodic compounding or specific charge structures related to outstanding balances. Therefore, the definition of continuous compounding as interest calculated and added to the principal at every moment accurately captures the essence of this financial concept.