APR to APY · Compound Interest · All Frequencies

APY Calculator

Calculate Annual Percentage Yield (APY) from any nominal rate. Compare daily, monthly, quarterly, and annual compounding. See how compounding frequency affects your actual earnings.

Last updated · 2026 rate environment checked against the Federal Reserve, FDIC and BLS

APR to APY Conversion
All Compound Frequencies
vs Simple Interest
Earnings for Any Period
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Enter your rate and compound frequency to calculate APY and earnings.

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APY vs APR Explained

APY is the rate you actually earn once compounding is included: APY = (1 + r/n)n − 1, where r is the stated annual rate and n the number of compounding periods a year. A 4.00% rate compounded daily is a 4.081% APY; compounded monthly it is 4.074%. Enter a rate, frequency and balance above to see the APY and the interest in dollars.

APR (Annual Percentage Rate) is the nominal interest rate without accounting for compounding. APY (Annual Percentage Yield) is the effective annual rate after compounding: it's what you actually earn. For savings and CDs, APY is always equal to or higher than APR.

For borrowing (credit cards, loans), APR is the stated cost. The effective rate you pay can be higher due to fees and compounding. This is why comparing APY-to-APY for savings and APR-to-APR for loans gives the most accurate picture.

Daily vs Monthly Compounding

At 5.00% APR: Daily (365x): APY = 5.127%. Monthly (12x): APY = 5.116%. The difference is only 0.011%, or about $1.05 a year on $10,000. Compounding frequency matters far less than the rate itself. A 5.00% daily beats a 4.90% monthly by far more than the compounding difference.

The Rule of 72

Divide 72 by the interest rate to estimate how many years to double your money. At 5% APY: 72/5 = 14.4 years to double. At 7%: 72/7 = 10.3 years. At 10%: 72/10 = 7.2 years. For borrowing: at 22% credit card rate: 72/22 = 3.3 years for debt to double if unpaid.

Continuous Compounding

The mathematical limit of compounding infinitely often is e^(r×t). At 5%: e^0.05 - 1 = 5.127%. Identical to daily compounding to 3 decimal places. No consumer product compounds continuously in practice: banks round to the nearest cent daily, which is effectively continuous.

Savings vs Loan APY

For savings: higher compounding frequency = higher effective return (good). For loans: higher compounding frequency = higher effective cost (bad). Credit cards compound daily at 20 to 29%, making the effective rate higher than the stated APR. This is why credit card balances grow so fast when unpaid.

APR to APY Conversion Table

Example nominal rates, not current offers. The APY rises with compounding frequency, but only slightly.

Nominal rateQuarterlyMonthlyDaily
1.00%1.004%1.005%1.005%
2.00%2.015%2.018%2.020%
3.00%3.034%3.042%3.045%
3.50%3.546%3.557%3.562%
4.00%4.060%4.074%4.081%
4.50%4.577%4.594%4.602%
5.00%5.095%5.116%5.127%

Going the other way: APY to APR

To find the nominal rate behind an advertised APY, use APR = n × ((1 + APY)1/n − 1). A 4.00% APY compounded monthly comes from a 3.928% nominal rate, and from 3.922% if compounded daily. You rarely need this for savings, since banks must quote APY, but it helps when an account or bond quotes only a nominal rate.

What an APY Earns on $10,000

Interest earned with no deposits or withdrawals. The first row is the FDIC national average savings rate for August 2026; the rest are example rates.

APYAfter 1 yearAfter 5 yearsAfter 10 years
0.38% (national average)$38$191$387
1.00%$100$510$1,046
2.00%$200$1,041$2,190
3.00%$300$1,593$3,439
4.00%$400$2,167$4,802
5.00%$500$2,763$6,289

The gap between an average account and a competitive one is far bigger than anything compounding frequency can add. Moving from daily to monthly compounding at 5% changes a year's interest on $10,000 by about $1.

Rates, Taxes and Inflation in 2026

Where rates stand

The Federal Reserve raised its federal funds target range by a quarter point to 3.75% to 4.00% in September 2026. Savings and money market APYs are variable and tend to follow that rate within weeks. CD rates are fixed once you open the CD. The FDIC's national averages for August 2026 were 0.38% for savings, 0.63% for money market accounts and 1.71% for a 12-month CD. Online banks usually pay well above those averages, so check each bank's current APY before you move money.

Your real return

Interest is taxed as ordinary income. A 4.00% APY taxed in the 22% bracket leaves 3.12%, and with consumer prices up 3.4% in the year to August 2026 (BLS CPI-U), the real return is slightly negative, about minus 0.27%. A high APY protects cash from inflation; it rarely grows it.

Rule of 72 check

Divide 72 by the APY to estimate the years it takes to double your money. At 4% that gives 18 years; the exact answer is 17.7.

Method and sources. APY = (1 + r/n)n − 1; APR = n((1 + APY)1/n − 1); interest after t years = balance × ((1 + APY)t − 1). All tables were computed with these formulas; rates shown are examples unless labelled. APY disclosure: Truth in Savings Act (Regulation DD). Rate environment: Federal Reserve FOMC statement, September 2026, and FDIC National Rates and Rate Caps, August 2026. Inflation: BLS CPI-U, August 2026 release.
APY calculations assume no fees, taxes, or changes to principal. Actual earnings depend on balance changes, rate fluctuations, and account-specific terms.

Frequently Asked Questions

APY stands for Annual Percentage Yield. It's the actual rate of return you earn on a savings account or CD in one year, accounting for compound interest. APY is always equal to or greater than the nominal rate (APR). For savings products, banks are required by Truth in Savings Act to disclose APY: it's the number to compare across institutions.

APY formula: APY = (1 + r/n)^n - 1, where r = nominal annual rate and n = number of compounding periods per year. Example: 5.00% APR compounded monthly: APY = (1 + 0.05/12)^12 - 1 = (1.004167)^12 - 1 = 5.116%. For daily compounding: (1 + 0.05/365)^365 - 1 = 5.127%.

APR (Annual Percentage Rate) is the stated nominal interest rate. APY (Annual Percentage Yield) is the effective annual rate after accounting for compounding. For savings accounts: APY > APR always (except with annual compounding, where they're equal). APY is the number that matters for comparing savings accounts. For loans, lenders use APR to disclose costs: the effective rate you pay may be higher.

More frequent compounding = higher effective yield. On $10,000 at 5.00% APR for 1 year: Annual compounding: $500 interest. Monthly: $511.62. Daily: $512.67. The difference between monthly and daily is only $1.05. The difference between annual and daily is $12.67: more meaningful. Over longer periods and higher balances, the compounding frequency effect compounds itself.

Rates vary widely by bank. The FDIC national average for savings accounts was 0.38% APY in August 2026, while online high-yield accounts typically pay several times that. Savings APYs are variable, and the Federal Reserve raised its target range to 3.75% to 4.00% in September 2026. Rates change with the Federal Reserve's benchmark rate. Check current rates before opening any account.

Always compare APY to APY, not APR to APR or APR to APY. Banks advertise APY for savings products as required by law. When comparing: confirm whether rates are promotional (time-limited) or standard, check minimum balance requirements, look for monthly fees that could eat into earnings, verify FDIC or NCUA insurance coverage. A 5.00% APY with a $25,000 minimum is less useful than a 4.85% APY with no minimum if you have less than $25,000.

Simple interest: I = P × r × t. On $10,000 at 5% for 3 years: $1,500 total. Compound interest (annual): $10,000 × 1.05^3 = $11,576 → $1,576 total. The $76 difference is 'interest on interest.' Over longer periods: 10 years at 5%, simple = $5,000 interest; compound = $6,289, a $1,289 difference. This gap grows dramatically over 20 to 30 years, which is why investing beats saving for retirement.

The bank applies your APY to your daily balance. Most HYSAs compound daily and credit interest monthly. If you deposit $10,000 at 5.00% APY daily compounding, you earn approximately $10,000 × 0.05/365 = $1.37 per day. After 30 days: ~$41.10. After a year: ~$512.67 (matches the APY calculation). Adding to the account increases the earning base; withdrawals reduce it.

For CDs: yes, APY is locked for the CD term. For HYSAs and money market accounts: no, APY is variable and changes with the Federal Reserve's benchmark rate. When the Fed cuts rates, HYSA rates typically drop within 1 to 2 months. When rates were near zero (2020 to 2022), HYSAs paid 0.5% or less. Always compare current rates; the highest APY advertised today may not be the highest next quarter.

Interest earned from savings accounts, CDs, and money market accounts is taxable as ordinary income in the year it's credited, even if you don't withdraw it. Banks send a 1099-INT for accounts earning $10+ in interest. Strategy: hold high-yield savings in a tax-advantaged account (IRA, HSA) to defer or eliminate taxes. Treasury securities (T-bills, I-bonds) pay federal income tax but are exempt from state and local taxes.

Use APR = n × ((1 + APY)1/n − 1), where n is the number of compounding periods per year. For a 4.00% APY compounded monthly: (1.04)1/12 is 1.003274, minus 1 is 0.003274, times 12 is 3.928%. With daily compounding the nominal rate is 3.922%. With annual compounding APR and APY are the same.

It is simply $10,000 times the APY. At an example 4.00% APY that is $400 for the year, at 3.00% it is $300, and at the FDIC national average savings rate of 0.38% (August 2026) it is $38. Because APY already includes compounding, you do not need to adjust for daily or monthly compounding. The interest is taxable in the year it is credited.
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