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EAR Formula:
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The Equivalent Annual Rate (EAR), also known as the Effective Annual Rate, represents the actual annual interest rate when compounding occurs more than once per year. It provides a standardized way to compare different investment or loan options with varying compounding frequencies.
The calculator uses the EAR formula:
Where:
Explanation: The formula accounts for the effect of compounding by calculating the interest earned on previously accumulated interest over multiple periods.
Details: EAR is crucial for comparing financial products with different compounding frequencies. It provides a true representation of the annual cost of borrowing or the annual return on investment, enabling better financial decision-making.
Tips: Enter the nominal APR as a decimal (e.g., 0.05 for 5%), and the number of compounding periods per year (e.g., 12 for monthly, 4 for quarterly, 365 for daily). Both values must be positive numbers.
Q1: What's the difference between APR and EAR?
A: APR (Annual Percentage Rate) is the nominal rate without considering compounding, while EAR (Effective Annual Rate) includes the effects of compounding and represents the true annual cost or return.
Q2: How does compounding frequency affect EAR?
A: More frequent compounding results in a higher EAR for the same nominal rate. For example, monthly compounding yields a higher EAR than annual compounding at the same nominal rate.
Q3: When is EAR most important to consider?
A: EAR is particularly important when comparing loans, credit cards, savings accounts, or investments with different compounding frequencies or when evaluating long-term financial products.
Q4: Can EAR be lower than the nominal rate?
A: No, EAR is always equal to or greater than the nominal rate. It equals the nominal rate only when compounding occurs annually.
Q5: How do I convert EAR back to nominal rate?
A: Use the formula: \( r = n \times ((1 + EAR)^{1/n} - 1) \), where r is the nominal rate and n is the compounding frequency.