The Advertised Rate Is Not the Whole Story
Banks advertise a nominal rate — the APR — but what actually lands in your account is the APY, the annual percentage yield. The difference is compounding: when interest gets added to your balance and starts earning its own interest, the true yearly return climbs above the headline number.
This free APY calculator converts any nominal APR into its true annual yield for your compounding schedule, then shows exactly what $10,000 earns at each rate. It also compares every compounding frequency side by side, so you can see whether “compounded daily” is a real advantage or just marketing.
What $10,000 earns in one year
| Compounding | APY | $10,000 after 1 year |
|---|
APY assumes the rate stays constant and interest compounds on schedule for a full year. Real accounts may credit interest differently and charge fees.
How to Use the APY Calculator
- Enter the nominal APR. Type the advertised annual rate as a plain number — 5 for 5%. This is the rate before compounding is factored in.
- Pick the compounding frequency. Choose how often interest is credited: annually, semiannually, quarterly, monthly, or daily. Match whatever your account actually does.
- Click Calculate APY. Your true annual percentage yield appears at the top, with the per-period rate and the “compounding boost” below.
- Check the $10,000 comparison. See what ten thousand dollars earns in one year at the nominal rate versus the true APY — and how much compounding adds.
- Scan the frequency table. It recalculates your APR at every compounding schedule, so you can compare a 4.75%-monthly account against a 5.00%-annual one in seconds.
What Is APY?
APY (annual percentage yield) is the real rate you earn on savings in a year, with compounding included. APR (annual percentage rate) is the nominal stated rate, with compounding left out. For anything that compounds, APY is always equal to or higher than the APR it came from.
Why does this matter? Because banks are required to disclose APY on deposit accounts, it is the only apples-to-apples way to compare two savings products. A bank quoting 4.90% compounded monthly actually pays about 5.01% APY — which beats a competitor’s flat 5.00% compounded annually. The headline rate alone would have steered you wrong.
On the borrowing side the roles flip: lenders quote APR, and you want that number as low as possible. For savings and CDs, chase the highest APY.
Disclosure law is what makes APY comparable: the Truth in Savings Act (Regulation DD) forces every bank to calculate deposit APY the same way, while loans follow the Truth in Lending Act — which is why borrowing costs are quoted as APR.
How Compounding Frequency Changes Your APY
The more often interest compounds, the more “interest on interest” you collect. But the gains taper off fast — most of the benefit arrives by monthly compounding. Here is what a 5.00% nominal rate becomes:
| Compounding | Periods/year | APY | $10,000 after 1 year |
|---|---|---|---|
| Annually | 1 | 5.000% | $10,500.00 |
| Semiannually | 2 | 5.063% | $10,506.25 |
| Quarterly | 4 | 5.095% | $10,509.45 |
| Monthly | 12 | 5.116% | $10,511.62 |
| Daily | 365 | 5.127% | $10,512.67 |
Daily compounding adds about $13 a year on $10,000 versus annual compounding. Nice to have — but a slightly higher rate matters far more than a fancier schedule. The calculator above rebuilds this table for any APR you enter.
The Formula
r = nominal annual rate as a decimal • n = compounding periods per year
Worked example. A savings account advertises 5% APR compounded monthly. Convert: r = 0.05, n = 12.
APY = (1 + 0.05/12)12 − 1 = (1.0041667)12 − 1 ≈ 5.116%. So $10,000 grows to about $10,511.62 in one year — $11.62 more than the nominal rate alone suggests.
Continuous Compounding: The Theoretical Ceiling
Compounding has a ceiling: as the periods per year grow without limit, (1 + r/n)n approaches er, so the maximum APY for nominal rate r is er − 1. At 5% that ceiling is ≈ 5.127% — exactly what daily compounding already yields.
Converting APY Back to APR
Work the formula backwards: APR = n × [(1 + APY)1/n − 1]. For 4.50% APY compounded daily: 365 × [(1.045)1/365 − 1] ≈ 4.402% APR. The nominal rate always sits below the APY it creates.
Limitations
- Assumes a constant rate. Many high-yield accounts are variable; if the bank cuts the rate mid-year, your actual yield drops with it.
- Ignores fees and minimums. Monthly fees, minimum-balance requirements, and withdrawal penalties all reduce what you actually keep.
- Nominal vs. effective confusion. APY is the effective rate for savers. Loan APRs work differently — they describe borrowing cost, not earnings — so never compare a loan APR directly against a savings APY.
- Taxes not included. Interest is generally taxable income, which trims the real return.
Tips for Getting the Best APY
- Always compare APY to APY. It is the only number that already includes compounding — comparing nominal rates across different schedules misleads.
- Rate beats frequency. A 5.10% APY compounded annually beats a 5.00% APY compounded daily, every time. Sort by APY first.
- Watch for teaser rates. Some accounts pay a high APY for a few months, then drop. Check what the rate becomes after the promotion.
- Consider the whole package. A slightly lower APY with no fees and no minimum balance can beat a higher APY that charges you to keep the account open.
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Frequently Asked Questions
What is the difference between APY and APR?
APR is the nominal stated rate without compounding. APY includes compounding, so it shows the true yearly return. For savings, APY is always equal to or higher than the APR it is based on.
How is APY calculated?
APY = (1 + r/n)n − 1, where r is the nominal rate as a decimal and n is the number of compounding periods per year. For example, 5% compounded monthly gives (1 + 0.05/12)12 − 1 ≈ 5.116% APY.
What is 5% APR compounded monthly in APY?
About 5.116%. On $10,000 that means roughly $511.62 of interest in one year instead of $500 — an extra $11.62 from monthly compounding.
Does daily compounding make a big difference?
Only a small one. At a 5% rate, daily compounding yields about 5.127% APY versus 5.000% with annual compounding — roughly $13 extra per year on $10,000. The headline rate matters far more.
Is a higher APY always better?
For savings, yes — with a caveat. Compare APY to APY, but also check fees, minimum balances, and whether the rate is a temporary promotion.
Can APY be lower than APR?
For deposit accounts, no — APY is always at least as high as the nominal rate. (Loan products use APR differently, so do not compare the two directly.)
Why do banks advertise APR instead of APY?
They advertise both, but the nominal rate often appears in bigger type. Regulators require the APY disclosure too — look for it in the fine print and compare on that number.
Is APY monthly or yearly?
Yearly — the A stands for annual. APY states a full year of earnings even when interest is credited monthly.
What does “compounded daily, credited monthly” mean?
Interest accrues daily but is deposited once a month. The APY is unchanged either way.
Will my APY change if the Federal Reserve changes rates?
Usually on variable-rate accounts — banks adjust APYs after Fed moves. Fixed-rate CDs keep their APY for the term.