A(t) = P e^{rt} for continuous compounding.
Key Concepts
- Concept: Continuous compounding grows exponentially
- Concept: Force of interest δ
- Concept: Link to effective rate i
Steps
- Action: Model with dA/dt = rA
- Action: Solve by separation of variables
- Action: Apply A(0)=P to get A(t)
Formula
$$A(t) = P e^{rt}$$
$$A(t) = P e^{delta t} quad text{where } delta text{ is the force of interest}$$
$$i = e^{delta} – 1$$
Example: P=1000, r=0.05, t=3 → A ≈ 1161.83