Final answer:
Continuous compounding refers to the concept where the number of compounding periods per payment period approaches infinity, applying a constant, instantaneous rate of interest calculation over time using an exponential formula based on the natural logarithm base.
Step-by-step explanation:
Continuous compounding means the number of compounding periods per payment period approaches the limit of infinity. This concept is a key idea in financial mathematics, where interest is calculated on an asset or liability. Unlike simple or periodic compounding, where the compounding occurs at discrete intervals, continuous compounding assumes that the compounding occurs constantly, at every possible instant in time.
With continuous compounding, the future value of an investment is calculated using the formula FV = Pe^(rt), where P is the principal amount, r is the annual interest rate in decimal form, t is the time in years, and e represents the base of the natural logarithm, approximately equal to 2.71828. As the number of compounding periods increases indefinitely, the formula simplifies to this exponential function using e, providing a more accurate measure of compounding effects over time.