APY Calculator
Convert a nominal rate into annual percentage yield
📊 Rate details
The stated (nominal) rate, before compounding - e.g. the APR a bank advertises.
Used to show the interest you'd earn in one year at this APY.
Last updated June 2026
Method: APY is computed with the standard formula (1 + r/n)n − 1, where r is the nominal annual rate and n is the compounding periods per year. The one-year interest figure compounds your balance at the chosen frequency at a constant rate.
Included: Effective annual yield, the compounding boost over the nominal rate, one-year interest on a balance, a simple-interest comparison, and an APY table across daily, monthly, quarterly, semiannual and annual compounding.
Not included: Taxes, additional deposits or withdrawals, rate changes over time, account fees, and bank-specific day-count or rounding rules. Results are estimates, not a financial offer.
APY calculator: everything you need to know
Suppose a savings account advertises a 5% nominal interest rate compounded monthly. The number that actually shows up in your account after a year is not 5% - it is the annual percentage yield (APY), which here works out to about 5.116%. On a $10,000 balance, that is roughly $511.62 in interest after one year, compared to $500 with simple interest - an extra $11.62 earned just from interest compounding on itself. This APY calculator turns any nominal rate and compounding frequency into the true yield so you can compare accounts apples-to-apples.
How APY is calculated
APY is the effective annual rate after compounding. The formula is:
APY = (1 + r ÷ n)n − 1 where r is the nominal annual interest rate written as a decimal (5% = 0.05) and n is the number of compounding periods per year (12 for monthly, 365 for daily, 1 for annual). Plugging in r = 0.05 and n = 12 gives (1 + 0.05/12)12 − 1 = 0.05116, or 5.116%. If interest is compounded only once a year, the formula collapses to APY = r, so the APY and nominal rate are identical.
APY vs. nominal rate vs. APR
The nominal rate is the stated rate before compounding. The APY folds in compounding and is what you actually earn on savings, so banks are required to disclose APY on deposit accounts. APR (annual percentage rate) is the figure usually quoted on loans and credit cards; it reflects fees but does not compound the rate the way APY does. If you are working with a loan or credit-card rate instead of a deposit, the APR Calculator is the right tool. When comparing two savings accounts, always compare their APYs, not their nominal rates - a 4.9% rate compounded daily can beat a 5.0% rate compounded annually.
Why compounding frequency matters (a little)
The more often interest compounds, the higher the APY climbs above the nominal rate - but with sharply diminishing returns. At a 5% nominal rate, the APY is 5.000% annually, about 5.095% quarterly, 5.116% monthly, and 5.127% daily. The biggest gain comes from moving away from annual compounding; beyond monthly, the extra yield is tiny. That is why the posted APY tells you far more than the compounding schedule alone, and why "daily compounding" marketing is rarely a decisive factor.
Using APY to compare accounts
- Compare APY to APY: it already includes compounding, so it is the single fairest number across accounts.
- Watch for introductory rates: a high APY that drops after a few months changes your real return - check how long it lasts.
- Mind the minimums: some top APYs apply only above a balance threshold or with direct deposit.
- Remember taxes: interest is usually taxable income, so your after-tax yield is lower than the posted APY.
How to use this calculator
The calculator turns a bank's quoted rate into the number that matters for your money. Follow these steps:
- Enter the nominal interest rate. Type the stated annual rate the bank advertises - for example, 5 for 5%. This is the "interest rate," not the APY; if the bank already gives you an APY, you do not need to convert anything.
- Choose the compounding frequency. Pick how often interest is added to the balance: daily, monthly, quarterly, semiannually, or annually. Most U.S. savings accounts and money market accounts compound daily or monthly; many certificates of deposit (CDs) compound monthly.
- Enter a balance. Add the amount you plan to deposit so the calculator can show the dollar interest you would earn in one year, not just the percentage.
- Read the results. The calculator shows the effective APY, the one-year interest in dollars, how much the compounding adds over a simple-interest baseline, and a side-by-side APY table across every compounding frequency at your rate.
Because every figure is recalculated instantly, you can try a few different rates and frequencies to see exactly where the extra yield comes from.
A second worked example
Imagine a high-yield savings account paying a 4.40% nominal rate compounded daily on a $25,000 balance. Using APY = (1 + r ÷ n)n − 1 with r = 0.044 and n = 365, the effective APY is about 4.498%. Over one year that balance earns roughly $1,124.50 in interest, versus $1,100 with plain simple interest - the daily compounding adds about $24.50. Now compare it to a competing account at a 4.50% nominal rate compounded annually: its APY is exactly 4.500%, essentially a tie. The lesson is that a slightly lower headline rate with frequent compounding can match a higher rate that compounds only once a year - which is precisely why the APY, not the nominal rate, is the number to compare.
Who this calculator is for
This tool is built for anyone weighing where to park cash and trying to compare offers on an even footing:
- Savers shopping for a high-yield account: convert each bank's quoted rate to APY so introductory teasers and different compounding schedules cannot disguise the real return.
- CD buyers: a CD's APY depends on both its rate and its compounding schedule; the CD Calculator lets you compare a 12-month CD against a savings account on equal terms.
- Money market and cash-management users: check whether daily compounding meaningfully changes your yield before chasing it - the Money Market Calculator applies the same idea to a money market balance.
- Students and anyone learning finance: see exactly how the compounding formula turns a nominal rate into an effective yield, step by step.
Key terms explained
- Nominal interest rate: the stated annual rate before compounding is applied. Also called the "stated rate" or simply the "interest rate."
- APY (annual percentage yield): the effective annual rate after compounding - the true one-year return on a deposit. This is the figure U.S. banks must disclose on deposit accounts under federal Truth in Savings rules.
- Compounding period (n): how many times per year interest is calculated and added to the balance. Common values are 365 (daily), 12 (monthly), 4 (quarterly), 2 (semiannual), and 1 (annual).
- Effective annual rate (EAR): a synonym for APY used more often in lending and corporate finance; the formula is identical.
- Simple interest: interest paid only on the original principal, with no compounding - the baseline the calculator compares APY against.
Factors that change your real yield
The posted APY is a starting point, not a guarantee. Several real-world factors push your actual return up or down:
- Variable rates: savings and money market APYs float with market conditions and can change without notice, so the rate you start with may not last the full year.
- Introductory or promotional APYs: a headline rate may apply only for the first few months, then revert to a much lower standard rate.
- Balance tiers and qualifications: the top APY may require a minimum balance, direct deposit, or a set number of transactions each month.
- Taxes: interest is generally taxable income reported on a Form 1099-INT, so your after-tax yield is lower than the posted APY - the higher your tax bracket, the bigger the gap.
- Fees: monthly maintenance or excess-withdrawal fees can quietly erode the interest you earn.
Tips to earn more from compounding
- Chase the APY, not the rate. A 4.9% rate compounding daily can beat a 5.0% rate compounding annually - convert both before deciding.
- Leave the interest in. Compounding only works if earned interest stays in the account; withdrawing it each month turns compound interest into simple interest.
- Watch the calendar on promos. Note when an introductory APY ends and be ready to move the money if the standard rate is uncompetitive.
- Use tax-advantaged space where it fits. Interest held in accounts such as an IRA is not taxed yearly, so more of the yield compounds for you.
- Re-check rates periodically. Because savings APYs move, a quick comparison every few months keeps your cash at a competitive yield.
Limitations and assumptions
So you can trust the numbers, here is exactly what this calculator does and does not model. It assumes a single deposit left untouched for a full year at a constant rate, compounding at the frequency you choose using the standard (1 + r ÷ n)n − 1 formula. It does not account for additional deposits or withdrawals during the year, mid-year rate changes, taxes, account fees, or bank-specific day-count conventions (some banks use a 360-day year or exclude leap days, which can shift the result by a few hundredths of a percent). For an ongoing savings plan with regular contributions, the Savings Calculator or Compound Interest Calculator is the better fit; for the rate quoted on a loan rather than a deposit, use the Interest Rate Calculator.
APY vs. simple interest vs. real return
It helps to keep three layers straight. Simple interest pays only on your principal - $10,000 at 5% earns a flat $500 a year, every year. APY adds compounding, so that same $10,000 at a 5% rate compounded monthly earns about $511.62 the first year because earlier interest starts earning interest too. Real (inflation-adjusted) return goes one step further: if your account yields 5.116% APY but prices rise 3%, your purchasing power grows only about 2%. APY tells you what the bank credits; subtracting taxes and inflation tells you what the money is actually worth to you. The calculator focuses on the first two layers, which are the ones that let you compare accounts fairly.
How it compares to related calculators
This page answers one focused question: "what is the true annual yield on this deposit?" If your question is slightly different, a sister tool fits better:
- To project a balance over several years, with or without monthly contributions, use the Compound Interest Calculator.
- To model a regular savings plan with recurring deposits, use the Savings Calculator.
- To compare certificate-of-deposit terms and maturity values, use the CD Calculator.
- To estimate yield on a money market balance, use the Money Market Calculator.
- To work backward from a known APY to the underlying nominal rate, or to solve for the rate on a deposit, use the Interest Rate Calculator.
- For a loan or credit-card rate that bundles in fees, compare the all-in cost with the APR Calculator.
Sources
- Consumer Financial Protection Bureau (CFPB) - guidance on APY, APR, and comparing deposit accounts.
- Federal Deposit Insurance Corporation (FDIC) - Truth in Savings Act (Regulation DD) disclosure rules for APY.
- Federal Reserve Board - Regulation DD and the standard APY calculation method.
- Internal Revenue Service (IRS) - taxation of interest income and Form 1099-INT.
⚠️ Common mistakes & edge cases
Comparing a nominal rate to an APY
A 5.00% nominal rate is not the same as a 5.00% APY. The nominal rate ignores compounding, so always convert both accounts to APY before deciding - otherwise you may pick the lower-yielding one.
Confusing APY with APR
APY is for what you earn (savings); APR is for what you pay (loans). They are calculated differently. Using an APR where you need an APY - or vice versa - will misstate your return.
Overvaluing daily compounding
At a 5% rate, daily compounding (5.127%) beats monthly (5.116%) by only about one hundredth of a percent. Don't let "compounds daily" marketing override a meaningfully higher posted APY elsewhere.
Forgetting the rate can change
Savings APYs are variable and can drop at any time, and introductory APYs expire. The one-year figure here assumes a constant rate, so a falling rate will lower your actual earnings.
❓ Frequently asked questions
What is APY?
APY stands for Annual Percentage Yield. It is the real rate of return on a deposit in one year, accounting for compounding. Unlike a plain nominal interest rate, APY includes the effect of interest earning interest, so it lets you compare savings accounts and CDs on an equal footing.
How is APY calculated?
APY = (1 + r/n)^n - 1, where r is the nominal annual interest rate as a decimal and n is the number of compounding periods per year. For example, a 5% nominal rate compounded monthly gives (1 + 0.05/12)^12 - 1 = 0.05116, or about 5.116% APY.
What is the difference between APY and APR?
APY (Annual Percentage Yield) is what you earn on savings and reflects compounding, so it is higher than the nominal rate. APR (Annual Percentage Rate) is typically what you pay on loans and does not compound the rate itself - it adds fees. Banks quote APY on deposits and APR on credit, which is why the two terms appear in different places.
Is APY always higher than the nominal rate?
Yes, whenever interest compounds more than once a year. If interest is compounded annually (once per year), the APY equals the nominal rate. The more frequently it compounds - quarterly, monthly, or daily - the higher the APY climbs above the nominal rate.
Does a higher compounding frequency really matter?
It helps, but with diminishing returns. At a 5% nominal rate, annual compounding yields 5.000% APY, monthly yields about 5.116%, and daily yields about 5.127%. The jump from annual to monthly is far larger than the jump from monthly to daily, so the stated APY matters more than chasing daily compounding.
Why does my bank's APY differ slightly from this calculator?
Small differences come from rounding and day-count conventions. Some banks use a 360-day year, exclude leap days, or round the posted APY to two decimals. This calculator uses the standard (1 + r/n)^n - 1 formula with the periods you choose, so expect results within a few hundredths of a percent of a bank's figure.
What does the one-year interest figure assume?
It assumes you deposit the balance once, leave it untouched, and let the interest compound at the chosen frequency for a full year at a constant rate. It does not include extra deposits, withdrawals, taxes, or rate changes. For ongoing contributions, use the Savings or Compound Interest calculator.
How do I convert APY back into a nominal rate?
Reverse the formula: r = n x ((1 + APY)^(1/n) - 1), where APY is written as a decimal and n is the compounding periods per year. For example, a 5.116% APY compounded monthly comes from a nominal rate of 12 x ((1.05116)^(1/12) - 1) = 0.05, or 5%. You only need this if a bank quotes an APY but you want the underlying rate for another calculation.
Is APY the same as effective annual rate (EAR)?
Yes. APY and effective annual rate (EAR) use the identical formula, (1 + r/n)^n - 1. 'APY' is the term U.S. banks use on deposit accounts, while 'EAR' (sometimes 'EAPR' or 'effective annual yield') shows up in lending, textbooks, and corporate finance. Whichever label you see, it means the true annual return after compounding.
Is the interest I earn taxable?
In most cases, yes. Interest from savings accounts, money market accounts, and CDs is generally taxable as ordinary income, and your bank reports it on Form 1099-INT if it totals $10 or more in a year. The APY shown here is before taxes, so your after-tax yield is lower - more so in a higher tax bracket. Interest earned inside a tax-advantaged account such as an IRA is not taxed each year.
Does a higher balance earn a higher APY?
The APY itself usually does not depend on your balance, so the percentage return is the same on $1,000 or $100,000 within a given account. However, some accounts use balance tiers where larger balances unlock a higher posted APY, and a few cap the top rate above a threshold. Always check the account's rate tiers - the calculator applies one APY to whatever balance you enter.
💡 Good to know
Banks must show you the APY
Under the federal Truth in Savings Act, U.S. banks and credit unions are required to disclose the APY (not just the nominal rate) on deposit accounts. That standardized number is what makes apples-to-apples comparison possible - this calculator simply reproduces it from a rate you have on hand.
Compounding has a ceiling
No matter how often interest compounds, the APY can never grow without limit. As compounding approaches continuous, a 5% nominal rate tops out near 5.127% (e0.05 − 1). That is why moving from monthly to daily compounding barely changes the result - you are already close to the mathematical maximum.
APY is a one-year snapshot
APY describes a single year of compounding at a constant rate. Over multiple years your money keeps compounding on the new, larger balance, so total growth outpaces a simple "APY times number of years" estimate. For multi-year projections, use the Compound Interest Calculator.