CONTINUOUS COMPOUNDING
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Compounding that occurs an infinite number of times per period, producing e^(rt) growth for rate r over time t.
Summary
Continuous compounding is a mathematical concept where interest is calculated and added to an investment an infinite number of times per period, rather than at discrete intervals like daily, monthly, or annually. This represents the theoretical limit of compounding frequency. The formula e^(rt) shows how an initial amount grows exponentially, where 'e' is Euler's number (≈2.718), 'r' is the annual interest rate, and 't' is time in years. While no real-world investment compounds truly continuously, this concept helps establish upper bounds for growth and simplifies certain financial calculations.
Usage Context
Understanding continuous compounding is crucial when comparing different investment options, calculating theoretical maximum returns, solving differential equations in finance, and working with exponential growth models in economics and finance courses.
Common Confusions
- Thinking continuous compounding means infinite money growth
- Confusing the base 'e' with a regular interest rate
- Believing the difference between continuous and daily compounding is enormous
- Mixing up the continuous compounding formula with simple interest
- Not understanding that 'r' must be expressed as a decimal, not percentage
