EAR Formula:
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The EAR (Effective Annual Rate) equation calculates the actual annual rate that an investment will earn due to compounding. It provides a way to compare different investment or loan options with different compounding periods.
The calculator uses the EAR equation:
Where:
Explanation: The equation accounts for the effect of compounding by raising the periodic rate to the power of the number of compounding periods.
Details: EAR is crucial for comparing different financial products with different compounding frequencies. It shows the true annual cost of a loan or true annual return on an investment.
Tips: Enter the nominal rate as a decimal (e.g., 0.05 for 5%), and the number of compounding periods per year (e.g., 12 for monthly). Both values must be positive.
Q1: Why use EAR instead of nominal rate?
A: EAR accounts for compounding effects, allowing accurate comparison between different compounding frequencies.
Q2: What's the difference between APR and EAR?
A: APR is the nominal rate without compounding, while EAR includes compounding effects.
Q3: How does compounding frequency affect EAR?
A: More frequent compounding leads to higher EAR for the same nominal rate.
Q4: What's the EAR for continuous compounding?
A: For continuous compounding, use \( e^i - 1 \) where e is Euler's number (~2.71828).
Q5: Can EAR be less than the nominal rate?
A: No, EAR is always equal to or greater than the nominal rate due to compounding.