Effective Annual Rate (EAR)
Converts a continuously compounded rate to an effective annual rate.
When to use: Use to find the effective rate when the stated rate is continuously compounded.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| EAR | Effective Annual Rate | True annual return | % |
| k | Continuous Rate | Continuously compounded rate | % |
Real-Life Examples
Example 1: Continuous to Effective
An investment earns 6% continuously compounded. What is the effective annual rate?
Given
Step-by-Step
6% continuous compounding is equivalent to 6.18% effective annual rate.
Example 2: High Rate Conversion
A volatile asset has a 15% continuous return. What is the effective annual return?
Given
Step-by-Step
15% continuous is equivalent to 16.18% effective annual rate.
Frequently Asked Questions
Raise Euler's number (e ≈ 2.71828) to the power of the continuous rate and subtract 1. For example, a 6% continuous rate gives EAR = e^0.06 - 1 = 0.0618, or 6.18% effective annual rate.
Yes. For a given nominal rate, continuous compounding produces the highest possible EAR. It is the mathematical limit as compounding frequency approaches infinity. However, the gap between daily and continuous EAR is negligibly small.
Continuously compounded rates are standard in options pricing (Black-Scholes model), quantitative finance, fixed-income analytics, and academic research. They are mathematically convenient because they are additive across time periods.