APY Calculator
Convert any nominal rate and compounding frequency into the effective annual yield — APY in the US, AER in the UK — the only number that fairly compares savings accounts.
One number that cannot hide the compounding
A nominal rate is an incomplete sentence — 5%… compounded how often? APY completes it: the actual percentage a balance grows in one year, compounding included. US banks must disclose it for deposit accounts; the UK calls the same figure AER. Either label, it is the only rate a saver should comparison-shop on.
APY = (1 + nominal rate ÷ m)m − 1, m = compounds per year
Example: 5% nominal compounded monthly: (1 + 0.05/12)12 − 1 = 5.12%. Compounded daily it reaches 5.13%; compounded yearly it is exactly 5.00%. A rival account at 5.05% nominal compounded yearly is worse than the 5% monthly account — a fact invisible until both are APYs.
For borrowers, the mirror is APR
APY describes money growing (savings). Money owed is described by APR, which folds in fees as well as compounding conventions. Confusing the two families — a loan quoted with an 'APY', say — is a reliable sign to slow down and read the document.
How this is calculated
APY = (1 + r/m)^m − 1 with r the nominal rate as entered and m the frequency selected (365 for daily). The growth-of-$10,000 line applies the same compounding for exactly one year so the percentage has a cash shadow. The AER option changes only the label, per the UK convention — the mathematics is identical, and the page says so.
Frequently asked questions
Why do banks advertise the nominal rate bigger than the APY?
For loans they advertise the (lower) nominal; for savings, US rules require the APY in ads — the honest number. Where you see a savings rate that is not labeled APY, ask which one it is.
Is APY guaranteed for a savings account?
The formula is guaranteed; the rate usually is not — most savings APYs are variable and move with the market. A CD's APY is fixed for its term, which is part of what the term buys.
Daily vs monthly compounding — worth switching banks for?
At 5%, the difference is about 0.013 percentage points — $1.30 a year on $10,000. Rate level and fees swamp frequency; choose on those.
What is AER exactly?
Annual Equivalent Rate — the UK (and EU) standardized effective rate for savings and also for overdrafts and credit, where it plays the APR-like role. Same compounding mathematics, different regulatory family.
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