Continuous compounding is the mathematical limit of compounding more and more often. It gives the maximum possible growth for a given nominal rate, though in practice it is only slightly more than daily compounding.
How to use the Continuous Compound Interest Calculator
- Initial balance
- Annual interest rate
- Term
- Additional deposits
- Deposit frequency
Results update as you type, and every field accepts the units shown in its menu.
How it works
Enter the initial balance, interest rate, term and any regular deposits.
Tips
- Use the nominal annual rate and pick the compounding frequency your bank or broker states.
- Small differences in return or fees compound into large differences over decades.
- Run the calculation with a cautious, a central and an optimistic return to see the range of outcomes.
- Past returns do not guarantee future returns – nothing here is investment advice.
Common mistakes to avoid
- Comparing an APR with an APY or effective rate.
- Ignoring inflation, taxes and fees when judging a real return.
- Entering a percentage as a decimal (5 instead of 0.05 is correct here).
Inputs explained
| Field | What to enter |
|---|---|
| Initial balance | Amount in your currency |
| Annual interest rate | In % |
| Term | Units: years, months |
| Additional deposits | Amount in your currency |
| Deposit frequency | Choose one: Monthly, Bi-weekly, Weekly, Quarterly … |
Example values
How the main result changes when Initial balance changes and everything else stays at the example values above:
| Initial balance | Final balance |
|---|---|
| 5,000 | 8,243.61 |
| 7,500 | 12,365.41 |
| 10,000 | 16,487.21 |
| 12,500 | 20,609.02 |
| 15,000 | 24,730.82 |
| 20,000 | 32,974.43 |
Formula
A = P × e^(rt)With deposits: + C × [(e^(r/f))^(f t) − 1] ÷ (e^(r/f) − 1)Effective annual rate = e^r − 1Worked example
Inputs — Initial balance: $10,000; Annual interest rate: 5 %; Term: 10 years; Additional deposits: $0; Deposit frequency: Never.
Results — Final balance = $16,487.21; Compound interest = $6,487.21; Effective annual rate = 5.1271 %; Same with monthly compounding = $16,470.09.
Frequently asked questions
What is continuous compounding?
Compounding infinitely often – the limit as the number of periods goes to infinity.
What is the formula?
A = Pe^(rt), where e ≈ 2.71828.
Is it much better than daily compounding?
No – the difference is a tiny fraction of a percent.
What formula does the Continuous Compound Interest Calculator use?
A = P × e^(rt).