📈 APY Calculator: Annual Percentage Yield from Any Rate
By ToolNimba Finance Team · Reviewed by ToolNimba Editorial Review, personal finance content · Updated 2026-06-23
This calculator gives an estimate only. The APY a bank actually pays can differ because of its exact compounding method, day-count convention, minimum balance rules, promotional or tiered rates, and fees. Rates also change over time. This is not financial advice, confirm the figures with your provider and speak to a qualified adviser before making decisions.
APY (annual percentage yield) is the real rate of return on a deposit once compounding is taken into account. Because interest earns interest, a 5% rate compounded monthly is worth more than a plain 5% paid once a year. Enter the nominal annual rate (the headline or APR figure) and how often it compounds, and this calculator shows the true APY plus the interest a balance would earn in a year.
What is the APY Calculator?
APY answers a simple question: if interest is added back to your balance during the year, what return do you actually end up with? The headline (nominal) rate, sometimes labelled APR on a savings product, ignores that effect. APY captures it. The more often interest compounds (daily rather than monthly, monthly rather than yearly), the more times interest is added back and starts earning interest itself, so the APY edges above the nominal rate. This is the whole reason two accounts quoting the same rate can pay you different amounts.
The formula is APY = (1 + r/n)^n - 1, where r is the nominal annual rate written as a decimal and n is the number of compounding periods per year. For a 5% rate compounded monthly, r = 0.05 and n = 12, giving (1 + 0.05/12)^12 - 1 = 0.051162, or 5.1162%. Compounded daily (n = 365) the same 5% becomes 5.1267%. Compounded just once a year (n = 1) the APY equals the nominal rate exactly, because there is no intra-year compounding to add. As n grows very large the APY approaches a ceiling set by continuous compounding, where APY = e^r - 1, so for 5% the absolute maximum is about 5.1271%.
The practical difference is usually small but real. On a $10,000 deposit at 5%, paying interest once a year gives $500, monthly compounding gives about $511.62, and daily compounding gives about $512.67. The jump from annual to monthly is far bigger than the jump from monthly to daily, which is why chasing daily over monthly compounding rarely matters much, while ignoring compounding entirely can mislead you. The gap also widens as the rate rises: at 1% the difference between annual and daily compounding is a few cents on $10,000, but at 10% it is several dollars.
APY matters most when you compare savings accounts, certificates of deposit (CDs), high-yield savings accounts, or money market accounts. Two accounts can quote the same nominal rate yet pay different amounts if one compounds daily and the other yearly. APY puts them on a single, comparable footing, which is why US banks are required under the federal Truth in Savings Act to disclose APY on deposit accounts. When you shop for a place to keep cash, the APY is the number to compare, not the interest rate.
The mirror term for borrowing is APR. On loans, credit cards, and mortgages you generally want a low APR, because that is the cost you pay. On savings you want a high APY, because that is the return you earn. The two are built from the same idea but point in opposite directions: APR is usually quoted before compounding (and may fold in fees on loans), while APY always bakes compounding in. Mixing them up is the single most common reason people misjudge how good a savings offer really is.
One more caveat: APY is a forward projection, not a guarantee. It assumes the rate, the balance, and the compounding schedule all hold steady for a full year. A variable rate that drops, a withdrawal mid-year, a promotional teaser rate that expires after three months, or a monthly fee can all pull your real return below the advertised APY. Use APY to compare offers on equal terms, then read the account's fine print to see whether you will actually capture it.
When to use it
- Comparing two savings accounts, CDs, or money market accounts that quote different compounding frequencies on a fair, like-for-like basis.
- Converting a quoted nominal rate (or APR) into the effective yield you will actually earn over a year.
- Estimating how much interest a given balance will earn in twelve months at a stated rate.
- Checking whether daily versus monthly compounding makes a meaningful difference on your deposit.
- Deciding between a high-yield savings account and a CD by putting both on a single APY basis.
- Sanity-checking a bank advertisement that quotes an interest rate but buries the APY in the fine print.
How to use the APY Calculator
- Enter the nominal annual interest rate as a percentage (the headline or APR figure).
- Choose how often the interest compounds, from annually up to daily.
- Optionally enter a starting balance to see the interest and ending balance after one year.
- Read off the APY, the nominal rate, the yearly interest, and the balance after one year.
- To compare two accounts, run each one in turn and pick the higher APY.
Formula & method
Worked examples
A savings account quotes a 5% nominal annual rate, compounded monthly.
- Write the rate as a decimal: r = 5 / 100 = 0.05
- Periods per year: n = 12
- r / n = 0.05 / 12 = 0.00416667
- (1 + 0.00416667)^12 = 1.0511619
- APY = 1.0511619 - 1 = 0.0511619 = 5.1162%
Result: APY of about 5.1162%, so $10,000 earns about $511.62 in a year, ending at $10,511.62
The same 5% nominal rate, but compounded daily instead of monthly.
- r = 0.05, n = 365
- r / n = 0.05 / 365 = 0.000136986
- (1 + 0.000136986)^365 = 1.0512675
- APY = 1.0512675 - 1 = 0.0512675 = 5.1267%
- On $10,000 the interest is 10,000 x 0.0512675 = $512.67
Result: APY of about 5.1267%, about $1.06 more than monthly compounding on $10,000
Comparing two accounts: Account A pays 4.90% compounded daily, Account B pays 4.95% compounded annually. Which is better?
- Account A: r = 0.0490, n = 365, so APY = (1 + 0.0490/365)^365 - 1 = 0.050212 = 5.0212%
- Account B: r = 0.0495, n = 1, so APY = (1 + 0.0495/1)^1 - 1 = 0.0495 = 4.9500%
- Compare the two APYs: 5.0212% versus 4.9500%
Result: Account A wins despite the lower headline rate, because daily compounding lifts its APY to 5.0212% versus 4.9500% for Account B
APY for a 5% nominal rate at different compounding frequencies
| Compounding | Periods per year (n) | APY |
|---|---|---|
| Annually | 1 | 5.0000% |
| Semi-annually | 2 | 5.0625% |
| Quarterly | 4 | 5.0945% |
| Monthly | 12 | 5.1162% |
| Weekly | 52 | 5.1246% |
| Daily | 365 | 5.1267% |
| Continuous | infinite | 5.1271% |
APY by nominal rate, compounded monthly versus daily
| Nominal rate | APY (monthly) | APY (daily) |
|---|---|---|
| 1% | 1.0046% | 1.0050% |
| 2% | 2.0184% | 2.0201% |
| 3% | 3.0416% | 3.0453% |
| 4% | 4.0742% | 4.0808% |
| 5% | 5.1162% | 5.1267% |
| 6% | 6.1678% | 6.1831% |
| 8% | 8.3000% | 8.3278% |
| 10% | 10.4713% | 10.5156% |
APY versus APR at a glance
| Feature | APY | APR |
|---|---|---|
| Used for | Savings, CDs, money market | Loans, credit cards, mortgages |
| Includes compounding | Yes, always | No, usually quoted before compounding |
| Better when | Higher (you earn more) | Lower (you pay less) |
| May include fees | No | Often, on loans |
| Equal to nominal rate when | Compounds once per year | No compounding involved |
Common mistakes to avoid
- Comparing accounts by nominal rate instead of APY. Two accounts can advertise the same headline rate yet pay different amounts because one compounds daily and the other yearly. Always compare by APY, which already folds in the compounding.
- Confusing APY with APR. APY measures what you earn on savings (higher is better) and includes compounding. APR usually measures the cost of borrowing (lower is better). On deposits the two only match when interest compounds exactly once a year.
- Forgetting that APY assumes the rate stays put. APY projects forward as if the rate and your balance held steady for a full year. A variable rate, a withdrawal, or a promotional rate that expires will all change the real return.
- Ignoring fees and minimum balance rules. Monthly fees or falling below a required minimum can wipe out the interest implied by a high APY. The advertised yield assumes you meet every condition the account sets.
- Overvaluing daily versus monthly compounding. The gap between daily and monthly compounding is tiny, often a hundredth of a percent. Chasing it while overlooking a fee or a lower headline rate is a poor trade.
- Forgetting that interest is usually taxable. APY describes the gross return before tax. In a regular (non-retirement) account the interest is typically taxable income, so your after-tax yield will be lower than the quoted APY.
Glossary
- APY
- Annual percentage yield, the effective yearly return on a deposit once compounding is included.
- Nominal rate
- The stated annual interest rate before compounding is accounted for, sometimes shown as APR on a savings product.
- Compounding frequency
- How many times per year interest is calculated and added to the balance (n in the formula).
- APR
- Annual percentage rate, typically the cost of borrowing. On a one-period deposit it equals the APY.
- Effective annual rate
- Another name for APY, the single yearly rate that reflects the actual return after compounding.
- Continuous compounding
- The theoretical limit where interest compounds infinitely often, giving APY = e^r - 1 and the highest possible APY for a rate.
- Principal
- The original amount deposited, before any interest is added.
- Truth in Savings Act
- US law requiring banks to disclose APY on deposit accounts so consumers can compare offers fairly.
Frequently asked questions
What is APY?
APY (annual percentage yield) is the real return on a deposit over a year once compounding is included. Because interest earns interest, the APY is at least as high as the nominal rate, and higher when interest compounds more than once a year.
How do I convert APR to APY?
Use APY = (1 + r/n)^n - 1, where r is the APR as a decimal and n is the number of compounding periods per year. For example a 5% APR compounded monthly gives (1 + 0.05/12)^12 - 1 = 5.1162% APY. This calculator does the conversion for you.
What is the difference between APY and APR?
APR is the nominal annual rate and is most often used for borrowing, where lower is better. APY adds the effect of compounding and is used for savings, where higher is better. They are equal only when interest compounds exactly once per year. On loans, APR may also fold in certain fees.
Why is APY higher than the nominal rate?
When interest compounds during the year, each addition starts earning interest itself. Those extra earnings on earlier interest push the effective yield above the nominal rate. The more frequent the compounding, the larger the gap.
Does more frequent compounding make a big difference?
It helps, but with diminishing returns. On a 5% rate, monthly compounding gives 5.1162% and daily gives 5.1267%, a difference of about a hundredth of a percent. The jump from yearly to monthly matters far more than monthly to daily.
Is a higher APY always better for savings?
A higher APY means more interest for the same balance, so all else equal it is better. But check the conditions: fees, minimum balance requirements, and promotional rates that expire can all reduce what you actually earn below the headline APY.
How much will $10,000 earn at 5% APY?
At a 5% APY, $10,000 earns about $500 in interest over one year, ending at roughly $10,500. If the 5% is a nominal rate compounded monthly, the APY is 5.1162%, so it earns about $511.62 and ends near $10,511.62.
How is APY calculated on a savings account?
The bank takes the nominal rate, divides it by the number of compounding periods, adds 1, raises the result to the power of the number of periods, and subtracts 1: APY = (1 + r/n)^n - 1. Most US savings accounts and CDs compound daily or monthly.
What is the highest APY a given rate can reach?
As compounding gets more frequent, APY approaches a ceiling set by continuous compounding, where APY = e^r - 1. For a 5% rate the maximum possible APY is about 5.1271%, so daily compounding (5.1267%) is already very close to the limit.
Is APY paid before or after tax?
APY is a gross figure quoted before tax. In a regular taxable account the interest you earn is generally taxable income, so your real after-tax yield is lower. Tax-advantaged accounts like an IRA can let the full APY compound untaxed until withdrawal.
Sources
- Annual Percentage Yield (APY) , Investopedia
- What is the difference between a loan interest rate and the APR? , U.S. Consumer Financial Protection Bureau
- What is APY and how is it calculated? , Fidelity