Continuous Compounding Calculator
Calculate growth when interest compounds continuously, using A = Pe^(rt).
About the Continuous Compounding Calculator
Enter the principal, the yearly rate and the number of years. The calculator gives the final amount, the interest and the effective yearly rate, and compares it with compounding once a year, monthly and daily.
Continuous compounding is the limit of compounding more and more often. It's the theoretical maximum for a given nominal rate and is used in finance (option pricing) and science (growth and decay).
The formula
A = P × e^(r·t)
- e
- 2.718281828…
- r
- yearly rate as a decimal
- t
- years
Worked example
10,000 at 5% for 10 years
- r × t = 0.05 × 10 = 0.5
- A = 10,000 × e^0.5 = 16,487.21
- Monthly compounding gives 16,470.09; effective yearly rate 5.1271%
Questions people ask
How much more than daily compounding?
Very little: at 5% on 10,000 over 10 years the difference is less than 1.
Where does e come from?
e = lim (1 + 1/n)ⁿ as n grows without limit.
How long to double with continuous growth?
ln 2 ÷ r, or 69.3 ÷ the rate in %: about 13.9 years at 5%.