How this instrument works
Nominal rates are labels; effective annual yield is what actually lands. Quote 12 percent, credit it once per year, and each dollar becomes 1.12 — label and result agree exactly. Credit that same 12 percent monthly and every crediting starts earning on interest already added, so each dollar reaches 1.126825 instead. APY names that second figure: what one unit of currency actually becomes across twelve months, assuming nothing is withdrawn along the way.
Shape of this formula follows from how nominal rates are written down. They are quoted per year but applied per period, so r gets sliced n ways into one period rate of r ⁄ n; multiplying by (1 + r ⁄ n) advances one period, and raising to n stacks twelve months of them. Subtracting 1 strips out your original stake and leaves growth alone. Finer slicing always helps, by shrinking amounts: 12 percent nominal gives 12.36 percent semi-annually, 12.5509 percent quarterly, 12.6825 percent monthly, 12.7475 percent daily — and never beats e^0.12 − 1 = 12.7497 percent, where infinitely fine slicing lands.
Every US bank quotes APY on deposit accounts because Truth in Savings, enacted in 1991 and implemented as Regulation DD, demands one standard figure so shoppers stop comparing incompatible nominal quotes. What that figure omits matters just as much: maintenance fees, balance tiers, tax on interest, teaser rates that reset after three months, and any assumption money stays put for twelve unbroken months. APY is arithmetic performed on your rate, not a forecast of your statement.
- Type your contract's quoted figure into Nominal annual rate, % — enter 12 for twelve percent, not 0.12.
- Set Compounding to match how often interest is credited: Annually, Semi-annually, Quarterly, Monthly or Daily.
- Read Effective annual yield, % — twelve months of growth on your balance, expressed in percentage points.
- Hold rate steady and cycle through Compounding to price frequency by itself: distance between Annually and Daily is what compounding is worth at that rate.
Worked example — 12% credited once per year
One twelve-month certificate quotes 12 percent and credits interest in a single lump at maturity. Put 12 into Nominal annual rate, % and choose Annually, which sets n = 1: (1 + 0.12 ⁄ 1)¹ − 1 = 0.12, so Effective annual yield, % reads exactly 12. Ten thousand dollars in, eleven thousand two hundred out. That identity is your baseline, and every other setting gets measured against it — with one crediting per year, label and result cannot diverge.
Now change nothing but Compounding, moving it to Monthly. Each month adds 1 percent to whatever balance stands, twelve rounds compound to 12.6825 percent, and that same ten thousand dollars finishes at $11,268.25 — sixty-eight dollars and change ahead of annual crediting, off an identical headline rate. Daily crediting stretches it to 12.7475 percent, or $1,274.75 of interest, and there it effectively stops: no schedule passes 12.7497 percent.
Questions
How is APY different from APR?
APY measures compounding and ignores fees; APR does close to reverse. Under Truth in Lending, card APR folds finance charges into an annualised cost yet is still quoted as one nominal rate, so a card advertising 24 percent that compounds daily on carried balances works out near 27.11 percent. Deposit products are disclosed as APY, credit as APR, and setting one beside another is not like-for-like.
Why does my bank's published APY differ slightly from this result?
Banks derive APY from interest actually paid over actual days, using Regulation DD's version: 100 × [(1 + interest ⁄ principal)^(365 ⁄ days) − 1]. February's short month, 360-day accrual bases, daily-balance versus average-balance methods, and rounding to two decimals each nudge published figures one basis point or so off pure formula output. Anything wider than that usually signals tiered rates, or promotional periods ending part-way through your year.
Does APY account for fees or tax?
Neither. A savings account paying 4.5 percent nominal compounded monthly shows 4.5940 percent here, worth $45.94 on $1,000 held all year. Five dollars monthly in maintenance fees removes $60 across those same twelve months, turning that gain into roughly $14 of loss — and interest earned is taxable income on top. Fees and tax sit outside this arithmetic entirely; subtract them yourself once you have read your yield.
Is daily compounding actually worth chasing?
Scale decides. At 1 percent nominal, moving from annual to daily crediting lifts yield from 1.0000 to 1.0050 percent — half of one basis point, five cents per year on $1,000. At 12 percent nominal that identical switch is worth 0.7475 percentage points, or $74.75 per year on $10,000. Crediting frequency multiplies against rate size, so it stays nearly invisible on small rates and turns material on large ones.
My bank only advertises APY — can I recover its nominal rate?
Yes, by inverting: r = n × [(1 + APY)^(1 ⁄ n) − 1]. Five percent APY credited monthly comes from nominal 4.8889 percent, which is what appears on rate sheets or in spreadsheet periodic-rate cells. Type that nominal figure into Nominal annual rate, %, leave Compounding on Monthly, and this instrument hands back 5 percent — one quick check that you read your disclosure correctly.
What happens if I enter 0.12 instead of 12?
You get 0.1201 percent rather than 12.6825 percent — plausible-looking, small, and therefore dangerous. Nominal annual rate, % takes percentage points, matching how contracts and rate sheets are written, so twelve percent is typed as 12. Division by 100 happens inside this formula already. When your result looks one hundred times too small, that entry is almost always why.
References
- CFPB — Bank accounts and services
- Federal Reserve — Selected Interest Rates (H.15)
- SEC investor.gov — Investing basics
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.