How the Effective Annual Yield Calculator works
Banks and lenders quote a nominal (stated) annual interest rate, but that number alone does not tell you the actual return you earn — or pay — over a year unless interest compounds exactly once annually. This calculator converts a nominal rate and a compounding frequency into the effective annual yield (EAY), the true percentage return after compounding is applied, using the standard formula financial institutions use to compute annual percentage yield (APY).
The formula
For a nominal annual rate r (as a decimal) compounded n times per year:
EAY = (1 + r/n)n − 1
For continuous compounding, the formula becomes the limit as n approaches infinity: EAY = er − 1, where e is Euler's number (≈ 2.71828). Once EAY is known, the future value of a principal P held for t years is FV = P × (1 + EAY)t.
Worked example
Take a 6% nominal annual rate compounded monthly (n = 12). The periodic rate is 0.06 / 12 = 0.005, and EAY = (1.005)12 − 1 ≈ 6.17%. A $10,000 principal held for one year grows to about $10,617 — $117 more than simple 6% simple interest would produce, purely from interest compounding on interest within the year.
Why compounding frequency matters
- Annual compounding (n = 1): EAY equals the nominal rate exactly — there is no intra-year compounding to add extra yield.
- More frequent compounding: monthly, weekly, and daily compounding each push EAY a little higher than the nominal rate, because interest starts earning interest sooner within the year.
- Diminishing returns: the jump from annual to monthly compounding is meaningful, but the jump from daily to continuous compounding is usually a rounding error — most of the compounding benefit is captured well before infinite frequency.
Where this formula applies
The same math underlies a savings account's advertised APY, a credit card's effective interest cost, and the effective annual rate (EAR) lenders use internally to compare loans quoted with different compounding schedules. This calculator performs the arithmetic only — it does not account for fees, taxes, promotional rate periods, or minimum balance requirements that can change what you actually receive or pay. Compare the stated APY on any account or loan disclosure with this calculation as a sanity check, not a substitute for the official disclosure.