Continuously Compounded Interest

Continuously Compounded Interest

Interest that is, hypothetically, computed and added to the balance of an account every instant. This is not actually possible, but continuous compounding is well-defined nevertheless as the upper bound of "regular" compound interest. The formula, given below, is sometimes called the shampoo formula (Pert^®).

Note: This same formula can be used for exponential growth and exponential decay.

Formula: A = Pe^(rt), where A = final amount, P = principle or original amount, r = rate of interest per year, t = time in years
Example: $2000 deposited at 12%/year compounded continuously for 7 years. A = 2000e^(0.12×7) = $4632.73

See also

Half-life, doubling time