Continuous Compounding Calculator

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

Inputs

Result

Loading calculator…
—

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.

Related calculators

Exponential Growth Calculator
A = A₀ · e^(kt) for continuous growth, or A = A₀ · (1 + r)^t for discrete.
Exponential Decay Calculator
A = A₀ · e^(-kt). Compute remaining quantity, half-life, or decay constant.
Logarithm Calculator
log_b(x) for any base b > 0, b ≠ 1, x > 0. Common bases shown side-by-side.
Antilogarithm Calculator
b^x — the inverse of a logarithm. Given the log value and base, recover the original number.
Exponent Calculator (b^x)
b^x — supports fractional, negative, and zero exponents.
Percentage Math Calculator
Calculate what X% of a value is, find what percentage one number is of another, or compute the percentage change between two numbers.

More tools you might like

Hand-picked tools that pair well with this one — same audience, same intent.

Logarithm Calculator
Calc

log_b(x) for any base b > 0, b ≠ 1, x > 0. Common bases shown side-by-side.

Antilogarithm Calculator
Calc

b^x — the inverse of a logarithm. Given the log value and base, recover the original number.

Exponential Growth Calculator
Calc

A = A₀ · e^(kt) for continuous growth, or A = A₀ · (1 + r)^t for discrete.

Exponential Decay Calculator
Calc

A = A₀ · e^(-kt). Compute remaining quantity, half-life, or decay constant.

Exponent Calculator (b^x)
Calc

b^x — supports fractional, negative, and zero exponents.

Compound Interest Calculator
Finance

Future value of an investment growing with compound interest plus monthly contributions, with a year-by-year line chart (linear or log scale) of balance vs. cumulative contributions.