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Continuous Compounding

A=P ertA = P \, e^{r t}
$
$
sig figs

Worked example: $1000 at 5% continuous for 10 → A = 1648.72. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

Where Continuous Compounding fits

Your answer feeds
Present Value
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See also

Compound Interest (Periodic): Both use final amount and principal amount.Simple Interest: Both use principal amount and interest rate per period.Present Value: Both use final amount and interest rate per period.Exponential Decay: Both use number of periods.Exponential Growth: Both use number of periods.
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Continuous Compounding explained

PArt

Continuous compounding is the limit of compounding ever more often: every instant, the balance grows in proportion to itself, giving A=PertA = Pe^{rt}. $5,000 at 4% per year for 10 years becomes 5000 × e⁰·⁴ ≈ $7,459.12, only a few dollars above monthly compounding: the compounding-frequency race hits a ceiling, and e is that ceiling.

The same law, with r negative, describes radioactive decay and drug elimination. Solving for t gives the exact doubling time t = ln 2 / r: at 4%, ln 2 / 0.04 ≈ 17.3 periods, which is where the banker's Rule of 72 comes from.

Continuous Compounding formula

A=P ertA = P \, e^{r t}
Where
  • AA= Final amount ($)
  • PP= Principal ($)
  • rr= Interest rate per period (decimal)
  • tt= Number of periods
In this toolkit

Time value of money

4 formulasSimple interest, periodic and continuous compounding, and discounting a future amount back to what it is worth today.

Revised 31 October 2026
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formula.expert. (2026, October 31). Continuous Compounding Formula & Calculator. https://formula.expert/solvers/continuous-compounding

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