\[A = Pe^{rt}\]
Variables
Acompound amount
Pprincipal amount
rannual interest rate
ttime period
Description
What is this formula?
The continuous compounding formula calculates the future value of an investment when interest is compounded continuously over time.
When to use it
Use this formula when interest growth is modeled as a continuous exponential process instead of periodic compounding.
Example
If 1500 USD is invested at an annual interest rate of 8% for 4 years:
A = 1500e^(0.08×4) ≈ 2064.85 USD
Applications
Financial mathematics, investment analysis, economic modeling, and exponential growth calculations.