Continuous Compounding Calculator
Continuous compounding, and the surprisingly small amount it adds over compounding once a year. It is the mathematical ceiling on frequency, not a different kind of growth.
Also called: e^rt calculator, exponential growth money.
$149,182.47 after 5 years. Compounding annually would give $146,932.81, so infinite compounding is worth only $2,249.66 more, which is the point of the exercise.
An estimate, not an offer or a guarantee. Projected returns assume the rate you entered holds for the whole term, which no market does.
This is what the calculation gives for the numbers you entered. It is an estimate, not advice, and it knows nothing about your situation beyond those numbers. Rules for United States change on a published schedule; the effective date is shown on every rule-based tool.
How this is calculated
Compounding more often earns more, but the gain converges: as the number of periods goes to infinity the factor approaches e to the power of the rate. At eight percent, annual compounding gives 8%, daily gives 8.33%, and continuous gives 8.33% as well to two places. The reason continuous compounding matters is not the extra money, it is that the exponential form makes the mathematics of options pricing and decay tractable.
value = principal * e ^ (rate * years)- P
- Principal (currency)
- r
- Annual rate (decimal)
- t
- Years (years)
Method and limits
What it assumes
- A constant rate.
What it deliberately does not model
- No deposit product actually compounds continuously. It is a modelling convenience.
Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator
Frequently asked questions
- Why use continuous compounding at all?
- Because e to the rt differentiates cleanly, which makes continuous-time finance workable. The extra return over daily compounding is negligible and is not the reason.
- What is the rule of 72 doing here?
- Under continuous compounding the exact doubling time is the natural log of two divided by the rate, about 69.3 over the rate as a percentage. The rule of 72 is a friendlier approximation of it.