Continuous Compounding Calculator
A = P · e^(rt) — the limit of compound interest as the compounding frequency → ∞.
Result
Final value
1,648.72
Interest earned: 648.72.
- FormulaA = P · e^(rt)
- Growth factor1.648721
- Effective annual ratee^r − 1, the discrete-equivalent annual rate.5.1271%
- Time10 years
Step-by-step
- A = 1000 × e^(0.05 × 10) = 1000 × e^(0.5000) = 1000 × 1.648721 = 1,648.72.
- Effective annual rate = e^r − 1 = e^0.05 − 1 = 0.0513 = 5.1271%.
How to use this calculator
- Enter principal, annual rate, and number of years.
- Read final value and effective annual rate.
About this calculator
Continuous compounding is the theoretical limit of compound interest: as compounding frequency increases (annual → quarterly → daily → continuously), the formula simplifies to A = Pe^(rt). For most rates, daily compounding is essentially indistinguishable from continuous (within ~0.0001%). Useful in physics and bond pricing.
Frequently asked
For 5% annual: monthly gives EAR = 5.116%, continuous gives 5.127%. The difference is small but matters for large principals or long time horizons.
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