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Effective Annual Rate Formula:
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The Effective Annual Rate (AER) or Annual Equivalent Rate represents the actual annual interest rate when compounding is taken into account. It provides a more accurate measure of the true cost of borrowing or the true return on investment compared to the nominal interest rate.
The calculator uses the AER formula:
Where:
Explanation: The formula accounts for the effect of compounding by calculating what the annual rate would be if interest were compounded only once per year but yielded the same final amount.
Details: AER is crucial for comparing different financial products with different compounding frequencies. It allows consumers and investors to make apples-to-apples comparisons between loans, savings accounts, and investments with varying compounding schedules.
Tips: Enter the annual nominal interest rate as a percentage (e.g., 5 for 5%), and the number of times interest is compounded per year. All values must be positive numbers.
Q1: What's the difference between nominal rate and effective rate?
A: The nominal rate doesn't account for compounding, while the effective rate shows the actual annual rate after compounding effects are considered.
Q2: How does compounding frequency affect AER?
A: More frequent compounding results in a higher effective annual rate, as interest is earned on interest more often.
Q3: When is AER most important to consider?
A: When comparing financial products with different compounding periods, or when evaluating long-term investments where compounding has significant effects.
Q4: Can AER be lower than the nominal rate?
A: No, AER is always equal to or higher than the nominal rate due to the compounding effect.
Q5: How is AER used in real-world applications?
A: Banks use AER to advertise savings account yields, credit card companies disclose effective rates, and investors use it to compare returns across different compounding investments.