Continuous Compounding (A = Pe^rt) Calculator
Continuous compounding represents the mathematical limit of discrete compounding as the number of periods per year approaches infinity, governed by Euler's constant e: A = P × e^((r/100)t).
Continuously compounded future value
Starting capital at t = 0
Continuously compounded force of interest in percent
Duration in years
Step-by-Step Calculation
Continuous compounding represents the mathematical limit of discrete compounding as the number of periods per year approaches infinity, governed by Euler's constant e: A = P × e^((r/100)t).
Real-World Reference Values
Standard continuous risk-free rate convention in derivatives
Equivalent discrete annual rate for continuous rate r
Exact ln(2) doubling constant
20-Row Comparison Table
Terminal Balance (A) · Initial Principal (P)
| # | Initial Principal ($) | Terminal Balance ($) | Δ % |
|---|---|---|---|
| 01 | 100 $ | 182.2119 $ | -99.00% |
| 02 | 10,000.00 $Current | 18,221.19 $ | 0.00% |
| 03 | 15,614.34 $ | 28,451.19 $ | +56.14% |
| 04 | 23,371.51 $ | 42,585.67 $ | +133.72% |
| 05 | 31,128.68 $ | 56,720.16 $ | +211.29% |
| 06 | 38,885.86 $ | 70,854.65 $ | +288.86% |
| 07 | 46,643.03 $ | 84,989.14 $ | +366.43% |
| 08 | 54,400.20 $ | 99,123.62 $ | +444.00% |
| 09 | 62,157.37 $ | 113,258.11 $ | +521.57% |
| 10 | 69,914.54 $ | 127,392.60 $ | +599.15% |
| 11 | 77,671.71 $ | 141,527.08 $ | +676.72% |
| 12 | 85,428.88 $ | 155,661.57 $ | +754.29% |
| 13 | 93,186.05 $ | 169,796.06 $ | +831.86% |
| 14 | 100,943.22 $ | 183,930.55 $ | +909.43% |
| 15 | 108,700.39 $ | 198,065.03 $ | +987.00% |
| 16 | 116,457.57 $ | 212,199.52 $ | +1064.58% |
| 17 | 124,214.74 $ | 226,334.01 $ | +1142.15% |
| 18 | 131,971.91 $ | 240,468.49 $ | +1219.72% |
| 19 | 139,729.08 $ | 254,602.98 $ | +1297.29% |
| 20 | 147,486.25 $ | 268,737.47 $ | +1374.86% |
Frequently Asked Questions
Why is continuous compounding used in quantitative finance?+
Continuous rates are time-additive and symmetric under natural logarithms, making them essential for Black-Scholes derivatives pricing and log-return modeling.
How much more does continuous compounding earn vs annual compounding?+
At r = 10% nominal, annual compounding yields 10.00%, whereas continuous compounding yields e^0.10 - 1 = 10.517%.
How do I compute the continuous log-return between two prices?+
Select r (%) as the target variable and enter P (starting price), A (ending price), and t (years).