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Effective Annual Rate Formula:
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The Effective Annual Rate (EAR) is the actual annual interest rate earned or paid on an investment or loan when compounding is taken into account. It provides a true comparison of different financial products with varying compounding periods.
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 different financial products with the same nominal rate but different compounding frequencies. It helps investors and borrowers understand the true cost or return of financial instruments.
Tips: Enter the nominal annual interest rate as a percentage and the number of compounding periods per year. Common compounding frequencies include: 1 (annual), 2 (semi-annual), 4 (quarterly), 12 (monthly), 365 (daily).
Q1: What's the difference between nominal rate and EAR?
A: Nominal rate doesn't consider compounding effects, while EAR reflects the actual annual return including compounding.
Q2: When is EAR higher than nominal rate?
A: EAR is always equal to or higher than the nominal rate. The more frequent the compounding, the higher the EAR compared to the nominal rate.
Q3: What is continuous compounding?
A: Continuous compounding uses the formula \( EAR = e^r - 1 \), where e is Euler's number (approximately 2.71828).
Q4: How does compounding frequency affect EAR?
A: Higher compounding frequency results in higher EAR for the same nominal rate, though the increase becomes smaller as frequency increases.
Q5: Is EAR the same as APY?
A: Yes, EAR is equivalent to Annual Percentage Yield (APY) in banking contexts, both representing the actual annual return including compounding.