Section 3.1: The Constant e and Continuous Compound Interest

The number e

e = limn → ∞(1 + 1/n)ⁿor, alternatively,e = lims → 0(1 + s)^1/s

Both limits are equal to 2.718 281 828 459 ...

Drag the slider to see the value of this expression for different values of s.

Simple, Compound, and Continuous Compound Interest

• Simple interest is calculated using A = P(1 + rt)
• Compound interest is calculated using A = P(1 + r/m)^mt
• Continuous compound interest is calculated using A = Pe^rt

where

• A = amount owed
• P = amount borrowed (the "principal")
• r = annual interest rate (a decimal)
• t = time in years
• m = number of compounding periods per year.

See the difference between simple and continuously compounded CD (certificate of deposit) rates for Goldman Sachs Bank.

Drag the sliders to change the annual interest rate r and the number m of interest compounding periods per year.