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Calculate EAR on Financial Calculator

EAR Formula:

\[ EAR = \left(1 + \frac{i}{m}\right)^m - 1 \]

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1. What is the EAR Equation?

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.

2. How Does the Calculator Work?

The calculator uses the EAR equation:

\[ EAR = \left(1 + \frac{i}{m}\right)^m - 1 \]

Where:

Explanation: The equation accounts for the effect of compounding by raising the periodic rate to the power of the number of compounding periods.

3. Importance of EAR Calculation

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.

4. Using the Calculator

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.

5. Frequently Asked Questions (FAQ)

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.

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