The continuous compounding formula is A = P e^{rt}.
Key Concepts
- Concept: Continuous compounding
- Concept: Principal, rate, time
- Concept: Exponential growth (Euler’s e)
Steps
- Action: Identify P, r, t
- Action: Compute A = P e^{rt}
- Action: Interpret result: A ≥ P if r,t ≥ 0
Formula
$$A = P e^{rt} quad text{where } A text{ is the amount after time } t,; P text{ is the principal},; r text{ is the annual rate (as a decimal).}$$