APY Calculator
Convert any nominal rate to APY, find the effective monthly and daily rate, and compare two savings accounts to see which earns more.
💰 What is APY (Annual Percentage Yield)?
APY (Annual Percentage Yield) is the actual annual rate of return on a deposit account after compounding is applied. It converts a nominal interest rate into the true percentage your money grows in one year, regardless of how frequently interest is credited. Banks are required by US Regulation DD to disclose APY on all deposit products so consumers can compare accounts on a level playing field.
APY is used in savings accounts, high-yield savings accounts (HYSAs), money market accounts, certificates of deposit (CDs), and treasury bills. It differs from APR (Annual Percentage Rate), which is the nominal rate used primarily for loans and credit cards. For any savings product, APY is always the number that matters for comparison because it captures the full effect of compounding. A bank offering 4.8% nominal compounded monthly actually delivers APY of 4.907%, while a competitor offering 4.9% compounded annually delivers exactly 4.9% APY. The second option is better despite the lower headline rate.
Common real-world applications include comparing high-yield savings accounts when parking an emergency fund, choosing between CDs with different terms and compounding schedules, evaluating money market account offers, and understanding the true yield on treasury and corporate bonds quoted at nominal rates. Financial advisors also use APY to illustrate how compounding frequency affects long-term wealth accumulation in tax-advantaged accounts.
A key distinction: APY is backward-looking for variable-rate accounts because the rate can change any time. For a 1-year CD with a locked rate, APY is a guaranteed yield. For a HYSA, the advertised APY reflects today's rate but the bank can cut it tomorrow. Always read whether a quoted APY is fixed (CD, treasury) or variable (savings account, money market) before making a deposit decision.
📐 Formula
APY = (1 + r ÷ n)n − 1
APY = Annual Percentage Yield (as a decimal; multiply by 100 for percent)
r = nominal annual interest rate as a decimal (e.g. 5% = 0.05)
n = number of compounding periods per year (365 daily, 12 monthly, 4 quarterly, 2 semi-annual, 1 annual)
Effective Monthly Rate = (1 + APY)1/12 − 1
Effective Daily Rate = (1 + APY)1/365 − 1
Example: r = 6% (0.06), n = 12 (monthly): APY = (1 + 0.06/12)12 − 1 = (1.005)12 − 1 = 0.06168 = 6.168%
📖 How to Use This Calculator
Steps
1
Enter the nominal interest rate. Type the annual interest rate exactly as the bank or institution advertises it. This is typically labeled APR or "stated rate," not APY. Use the slider or type directly.
2
Select compounding frequency. Choose how often the bank credits interest: daily (most online HYSAs), monthly (common for CDs), quarterly, semi-annual, or annual. This information is in the account disclosure or product terms.
3
Read your APY and effective rates. The result panel shows APY, effective monthly rate, effective daily rate, and how much more the APY exceeds the nominal rate. This lets you compare any two savings products on equal terms.
4
Switch to Compare Accounts mode. For a side-by-side analysis, click "Compare Accounts," enter your deposit amount, the rate and compounding frequency for each account, and the term in years. The calculator shows which account earns more and by how much in dollars.
💡 Example Calculations
Example 1 - Online HYSA at 5% Nominal, Daily Compounding
Marcus by Goldman Sachs offers 5.00% APY compounded daily. What is the true annual yield?
1
Identify inputs: r = 0.05 (5%), n = 365 (daily compounding).
2
Apply the formula: APY = (1 + 0.05/365)365 - 1 = (1.0001370)365 - 1.
3
Result: APY = 0.051267, or 5.1267%. On a $20,000 deposit, this yields $1,025.34 in one year versus $1,000.00 from a 5% annual simple-interest account.
APY = 5.1267% (nominal rate was 5.00%)
Try this example →Example 2 - Bank CD at 4.75% Nominal, Monthly Compounding
A 12-month CD pays 4.75% nominal compounded monthly. What APY does the investor actually earn?
1
Inputs: r = 0.0475, n = 12 (monthly). Monthly rate = 0.0475/12 = 0.003958.
2
APY = (1 + 0.003958)12 - 1 = (1.003958)12 - 1.
3
APY = 1.04849 - 1 = 0.04849, or 4.849%. On a $50,000 CD, the investor earns $2,424.50 in 12 months, not the $2,375 the nominal rate would suggest.
APY = 4.849%
Try this example →Example 3 - Comparing Two Savings Accounts Over 5 Years
Account A: 4.50% daily compounding. Account B: 4.65% monthly compounding. $25,000 deposit for 5 years. Which wins?
1
Account A APY: (1 + 0.045/365)365 - 1 = 4.603%. Account B APY: (1 + 0.0465/12)12 - 1 = 4.758%.
2
Balance A after 5 years: $25,000 x (1.04603)5 = $31,143.18. Balance B: $25,000 x (1.04758)5 = $31,371.82.
3
Account B wins by $228.64 despite daily compounding on Account A. The higher nominal rate on B overcomes the more frequent compounding advantage on A.
Account B wins: $228.64 more over 5 years
Try this example →❓ Frequently Asked Questions
What is APY and how is it different from APR?
APY (Annual Percentage Yield) is the actual annual return on a deposit after compounding. APR is the nominal rate, used mainly for loans. For savings accounts and CDs, APY is always the right number to compare because it reflects true annual growth. A 5% APR compounded monthly gives APY of 5.116%, so you earn more than the stated rate suggests.
How do I calculate APY from a nominal interest rate?
Use the formula: 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 (365 daily, 12 monthly, 4 quarterly, 2 semi-annual, 1 annual). For a 6% nominal rate compounded monthly: APY = (1 + 0.06/12)^12 - 1 = 6.168%. This calculator does the arithmetic instantly for any rate and frequency.
Which compounding frequency gives the highest APY for the same nominal rate?
More frequent compounding always produces higher APY. The ranking from highest to lowest is daily, monthly, quarterly, semi-annual, then annual. For a 5% nominal rate: daily APY = 5.127%, monthly = 5.116%, quarterly = 5.095%, semi-annual = 5.063%, annual = exactly 5.000%. The theoretical maximum is continuous compounding at APY = e^r - 1 = 5.127%, essentially equal to daily.
Is a higher APY always better for a savings account?
Yes, for identical terms and equivalent insurance coverage. The only exceptions are accounts with minimum balance requirements, early-withdrawal penalties, or introductory promotional rates that reset to a much lower base rate. Always check whether the advertised APY is a bonus rate valid for 3 to 6 months or a permanent ongoing rate before moving large deposits.
How much does compounding frequency actually matter in dollar terms?
On a $10,000 deposit at 5% nominal for 1 year, annual compounding earns $500.00, monthly earns $511.62, and daily earns $512.67. The difference between daily and annual is only $12.67. Over 10 years, daily compounding produces $197.70 more than annual on $10,000 at 5%. The difference grows with larger balances and longer terms but is rarely the deciding factor when comparing real savings products.
What is the difference between APY and effective annual rate (EAR)?
APY and EAR are the same calculation. APY is the US regulatory term for deposit accounts (Regulation DD). EAR or EFF% is the equivalent term in finance textbooks and international contexts. European banks quote AER (Annual Equivalent Rate), which is also identical. All three use (1 + r/n)^n - 1. The different labels exist because of different regulatory contexts, not different math.
Does APY account for taxes on interest income?
No. APY is a pre-tax measure. Interest from savings accounts and CDs is taxable as ordinary income in the US. To find after-tax APY, multiply APY by (1 minus your marginal tax rate). At 5.00% APY in the 22% bracket, after-tax APY is approximately 3.90%. Tax-advantaged accounts such as Roth IRA or HSA preserve the full pre-tax APY because qualifying withdrawals are tax-free.
What APY should I expect from a high-yield savings account today?
In mid-2025, competitive high-yield savings accounts at online banks and credit unions offered APYs from approximately 4.50% to 5.25%. Traditional brick-and-mortar banks typically offered 0.01% to 0.50% APY. HYSA rates track the Federal Reserve benchmark rate closely and can change within days of a Fed meeting. Compare current rates at multiple institutions before depositing, as the spread between top and bottom accounts is often 10x or more.
How do I compare two savings accounts with different compounding schedules?
Use the Compare Accounts mode on this calculator. Enter your deposit amount, the nominal rate and compounding frequency for each account, and the term in years. The tool converts both to APY and projects the exact final balance and interest earned for each. This is the only reliable comparison method because headline rates are often stated at different compounding frequencies, making direct rate comparison misleading.
Can APY be negative?
Yes, mathematically. Several European central banks imposed negative interest rate policies between 2014 and 2022, resulting in negative APY on some deposits and government bonds. Depositors paid the bank to hold their money. No US retail bank has ever charged negative APY on consumer deposits, but large institutional deposits were subject to negative rates at some international banks during this period.
How do I convert APY back to a nominal rate?
Use the reverse formula: r = n x ((1 + APY)^(1/n) - 1). For a CD advertising 5.127% APY compounded daily (n=365): r = 365 x ((1.05127)^(1/365) - 1) = approximately 5.00% nominal. This reverse calculation is useful when comparing bonds or instruments that quote APY at different compounding frequencies and you need a common nominal rate for comparison.
Why do banks advertise APY for deposits but APR for loans?
US regulations require banks to use APY for deposit products (Regulation DD) and APR for credit products (Truth in Lending Act). For deposits, APY is the higher number because compounding works in the depositor's favor. For loans, APR is the lower number and excludes certain fees, making loans look cheaper than they are. This asymmetry is intentional: APY makes savings products look more attractive, APR makes borrowing costs look lower. Always use APY to compare savings and APR (plus fees) to compare loans.