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Effective Annual Rate Calculator (APY)

Convert a nominal annual interest rate into its true effective annual rate (APY) for a given compounding frequency.

Nominal annual rate
12%
Effective annual rate (APY)
12.6825%
Difference from nominal rate
0.6825% points

How it works

A nominal (stated) annual rate doesn't tell the whole story once interest compounds more than once a year — each compounding period earns interest on interest already added earlier in the year. The effective annual rate (EAR, also called APY) captures the true annual growth: EAR = (1 + r/n)ⁿ − 1, where r is the nominal rate as a decimal and n is the number of compounding periods per year.

Continuous compounding is the limiting case as n grows without bound, which converges to EAR = eʳ − 1 (Euler's number e ≈ 2.71828) — it's a standard textbook idealization for comparison, not a rate any real account compounds at, since no institution actually compounds infinitely often.

With annual compounding (n = 1), the effective rate always equals the nominal rate exactly — there's only one compounding period, so there's no within-year interest-on-interest to create a gap between the two.

FAQ

Why is the effective rate always higher than the nominal rate?

Because compounding more than once a year means some interest starts earning its own interest before the year is up, which only ever adds to the total — it can't subtract from it. The gap grows with both the nominal rate and the compounding frequency, which is why a 12% rate compounded daily (≈12.7475%) ends up closer to the continuous-compounding limit than the same rate compounded monthly (≈12.6825%).

Is this the same as APY on a savings account?

Yes — APY (annual percentage yield) is the same concept as effective annual rate, just the term more commonly used for savings and deposit accounts, while EAR is more common in general finance. Both express the true one-year return once compounding is accounted for.

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