Continuous compounding calculator
Continuous compounding is the upper limit of growth for a given nominal rate and appears often in finance and maths courses.
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How to use it
- Enter principal, annual interest rate and term.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
A = P × e^(r × t), where e ≈ 2.718282. Effective annual rate = e^r − 1.
Example
Inputs: Principal = 1,000 your currency, Annual interest rate = 5 %, Term = 10 years. Result: Final amount: 1,648.72; Total interest: 648.72; Effective annual rate: 5.1271%.
Limits and caveats
- No bank account literally compounds continuously; treat the result as a theoretical upper bound.
- Assumes a fixed rate with no deposits or withdrawals.
Questions about this tool
What is e?
A mathematical constant of about 2.718282, the limit of (1 + 1/n)^n as n grows without end.
How much more than daily compounding is it?
Very little. At 5%, daily gives 5.1267% and continuous 5.1271%.
Where is continuous compounding used?
In option and bond pricing models and in growth and decay problems in maths.