Effective Annual Yield (EAY) Calculator
Calculate the Effective Annual Yield (EAY) — the true annualized return on an investment that accounts for the effect of intra-year compounding — to compare investments with different compounding frequencies on an equal basis.
How to use this tool
- Enter nominal (stated) annual rate and compounding periods per year in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your effective annual yield (eay) and the full breakdown beneath it.
⚠ This tool provides general estimates for education only and is not financial, tax or legal advice. Figures may not reflect your situation — verify with a qualified professional.
Formula
Periodic Rate = Nominal Rate ÷ n
EAY = (1 + Nominal Rate / n)n − 1
where n = number of compounding periods per year.
How it works
The Effective Annual Yield converts a nominal interest rate — which does not account for intra-year compounding — into the equivalent rate that would apply if interest compounded once per year. Each compounding period adds interest to the growing balance, so interest earns interest within the year, resulting in an effective yield higher than the stated nominal rate. This standardized rate allows direct comparison between products compounding at different frequencies, such as a monthly-compounding savings account versus a quarterly-compounding bond.
Worked example
Monthly compounding at 6% nominal rate
- Nominal Rate = 6%; Compounding periods per year (n) = 12
- Periodic Rate = 6% ÷ 12 = 0.5% per month
- EAY = (1 + 0.005)^12 − 1 = 1.061677812... − 1 = 0.061678 = 6.1678%
Effective Annual Yield = 6.1678%
Common mistakes to avoid
- Confusing EAY with the nominal rate — they are equal only when compounding is annual (n=1); at higher frequencies EAY always exceeds the nominal rate.
- Using the wrong value of n for the investment type — Treasury bills use a 360-day convention in some contexts, while savings accounts typically use 365, and mixing them gives different EAY values.
- Comparing investments with different compounding frequencies using nominal rates alone, which understates the advantage of more-frequently compounded products.
Key terms
- What is the difference between nominal rate and effective annual yield?
- The nominal rate is the stated annual rate without accounting for compounding within the year. The EAY reflects the actual annual growth rate once intra-year compounding is included.
- What is the Effective Annual Rate (EAR)?
- EAR and EAY are the same concept. EAR is commonly used for borrowing costs; EAY is often used for investment returns, but the formula is identical.
- How does compounding frequency affect the yield?
- More frequent compounding increases the effective yield for the same nominal rate because interest is calculated and added to principal more often, allowing earlier interest to earn additional interest.
- What is continuous compounding?
- Continuous compounding is the limiting case where n approaches infinity. The effective yield under continuous compounding equals e raised to the power of the nominal rate, minus 1 (e.g., e^0.06 − 1 ≈ 6.184% for a 6% nominal rate).
Frequently asked questions
- What is the difference between EAY and EAR?
- EAY and EAR (Effective Annual Rate) are the same concept — the true annualized yield accounting for compounding. EAY is the term more often used in investment contexts, EAR in lending contexts.
- Does EAY account for reinvestment risk?
- The EAY formula assumes coupon or interest payments are reinvested at the same periodic rate. If market rates change, actual realized yield will differ from the stated EAY.
- How do I compare a monthly-compounded savings account to an annually-compounded bond?
- Convert both to EAY using the formula EAY = (1 + r/n)^n - 1. The product with the higher EAY provides the better return for the same nominal rate.