Continuous Compounding Calculator

A = P · e^(rt) — the limit of compound interest as the compounding frequency → ∞.

Inputs

Result

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General calculation reads

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Jordan Ellenberg - math thinking
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Scientific calculator (Casio fx-991EX)
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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

How different is continuous from monthly compounding?+
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.
Where is continuous compounding used in practice?+
In finance theory (Black-Scholes), bond pricing, and physics (radioactive decay, capacitor discharge). Most consumer banking uses monthly or daily compounding.
What is the effective annual rate (EAR)?+
The rate that gives the same total return when compounded annually. For continuous: EAR = e^r − 1.
Continuous compounding vs APY?+
APY is typically the discrete EAR your bank advertises, often monthly or daily compounded. Continuous EAR (e^r − 1) is slightly higher.
Is e^(rt) the same as Pert?+
Yes — written without a multiplication sign, e^rt and Pert are the same formula.

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