Continuous Compounding Calculator
What happens when interest compounds at every instant?
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Continuous Compounding Calculator by TheCalcTools
How the Continuous Compounding Calculator works
Enter the principal, nominal annual rate and number of years.
Continuous compounding uses Euler’s number e in place of repeated discrete periods.
It is the theoretical limit of compounding more and more often.
The formula
Worked example
Using the default values shown in the calculator:
| Principal | $10000 |
|---|---|
| Annual rate (%) | 5 % |
| Years | 10 |
- A = 10,000 × e^(0.05 × 10) = $16,487.21.
- Annual compounding gives $16,288.95, a difference of $198.27.
Result:
| Value, continuous compounding | $16,487.21 |
|---|---|
| Value, annual compounding | $16,288.95 |
| Difference | $198.27 |
| Effective annual rate | 5.13% |
Frequently asked questions
Is continuous compounding used in practice?
Rarely for consumer products, but it is widely used in financial mathematics, such as option pricing, because it is easier to work with.
How much more does it earn?
Very little compared with daily compounding. The difference from annual compounding grows with rate and time.
Sources and further reading
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