🧮 Continuous Compound Interest Calculator
Calculate growth using A = P · e^(r·t)
How to Use This Calculator
Enter Principal
Provide the starting amount (P).
Enter Annual Rate
Provide r as a percentage (e.g., 5 for 5%).
Enter Time in Years
Provide t in years (e.g., 10).
Calculate
Click Calculate to see A and interest earned.
Formula
A = P · e^(r·t)
Interest = A − P
Example: P = $10,000, r = 5% (0.05), t = 10 years
A = 10000 · e^(0.05·10) = 10000 · e^(0.5) = 10000 · 1.64872 = $16,487.21
Interest = 16,487.21 − 10,000 = $6,487.21
About Continuous Compounding
Continuous compounding assumes interest is added at every instant. It produces slightly higher amounts than discrete compounding at the same nominal rate.
When to Use
- Modeling theoretical upper-bound growth
- Pricing in finance and certain derivatives
- Comparing with discrete compounding at high frequencies
- Teaching exponential growth concepts
Why Use Our Calculator
- ✅ Instant, accurate e^(rt) calculations
- ✅ Clear inputs and breakdown
- ✅ Mobile friendly and free
Tips
- Use decimal rate in the formula (e.g., 5% → 0.05)
- Ensure time is in years for annual rate
- For discrete compounding, use our standard compound calculator
Frequently Asked Questions
What does e mean?
e ≈ 2.71828 is the base of natural logarithms and appears in continuous growth processes.
Is continuous compounding realistic?
It’s a useful idealization. Real products compound discretely (daily/monthly), but continuous is a close upper bound.
How does it compare to daily compounding?
Continuous yields slightly more than daily compounding at the same nominal rate. The difference shrinks as frequency increases.
Can r be negative?
Yes; a negative r models continuous decay (amount declines over time).