APY Calculator

Convert a nominal interest rate into Annual Percentage Yield (APY) based on how often it compounds. See your true annual yield and the real interest earned on any balance — for savings, CDs & HYSAs.

💹

APY Calculator

Annual Percentage Yield

%
$
Annual Percentage Yield (APY)
Nominal Rate (APR)
APY − APR Boost
Interest in 1 Year
Balance After 1 Year

APY vs APR — What's the Difference?

APY (Annual Percentage Yield) is the real rate of return you earn on savings in one year once compounding is included. The nominal rate (APR) ignores compounding, so APY is always equal to or higher than the stated rate. The formula is APY = (1 + r ÷ n)n − 1, where r is the nominal annual rate and n is the number of compounding periods per year. A 5% rate compounded daily yields an APY of about 5.13%.

Banks advertise savings accounts and CDs in APY because it's the honest, comparable figure — it already bakes in how often interest is added. When comparing high-yield savings accounts (HYSAs) or certificates of deposit, always compare APY to APY. The more frequently an account compounds (daily beats monthly beats annually), the higher the APY for the same nominal rate, though the difference is small at typical rates.

📈

APY Includes Compounding

APY = (1 + r/n)ⁿ − 1. It reflects interest-on-interest, so it's always ≥ the nominal APR.

🏦

Compare Apples to Apples

Banks quote savings & CDs in APY. Always compare APY to APY across accounts — never APY vs APR.

🔁

Frequency Matters

Daily compounding yields slightly more than monthly or annual for the same rate — but the gap is small.

Formula & Logic

Annual percentage yield expresses what a nominal interest rate actually earns once compounding is taken into account, which makes it the only fair basis for comparing savings products. Two accounts quoting 5% are not equivalent if one compounds daily and the other annually. US banks are required by the Truth in Savings Act to disclose APY precisely so that consumers can compare like with like. The counterpart on the borrowing side is APR, which works the opposite way — it adds fees into a rate rather than adding compounding — so APY and APR are not symmetrical despite the similar names.

APY = (1 + r/n)^n − 1Continuous compounding: APY = e^r − 1Reverse: r = n × [ (1 + APY)^(1/n) − 1 ]

where:

r
nominal annual rate, as a decimal
n
compounding periods per year (365 daily, 12 monthly, 4 quarterly, 1 annual)
e
Euler's number, 2.71828 — the limit as compounding becomes continuous

Assumptions: APY assumes the rate holds for a full year and interest stays in the account. Variable-rate savings accounts can change the rate at any time, so a quoted APY is a snapshot rather than a promise.

Step-by-Step Example: 5% Nominal at Four Compounding Frequencies

The same headline rate, compounded four different ways, on a $10,000 deposit.

  • Nominal rate5.00%
  • Deposit$10,000
  1. Annual (n=1): (1 + 0.05/1)^1 − 1 = 5.0000% → $500.00.
  2. Quarterly (n=4): (1 + 0.0125)^4 − 1 = 5.0945% → $509.45.
  3. Monthly (n=12): (1 + 0.0041667)^12 − 1 = 5.1162% → $511.62.
  4. Daily (n=365): (1 + 0.05/365)^365 − 1 = 5.1267% → $512.67.
  5. Continuous: e^0.05 − 1 = 5.1271% → $512.71.
  6. Note the ceiling: daily is within half a cent of continuous, so more frequent compounding adds nothing.

Result5% nominal = 5.13% APY compounded daily

The whole range from annual to continuous is only 12.7 basis points, or $12.71 on $10,000. Compounding frequency is worth checking but is far less important than the rate itself — a bank offering 5.1% annually beats one offering 5.0% daily.

FAQ

APR (nominal rate) is the stated annual rate without compounding. APY (yield) includes compounding, so it shows what you actually earn in a year. For savings you want a high APY; for loans you want a low APR. APY is always equal to or greater than the nominal rate it's based on.
APY = (1 + r ÷ n)ⁿ − 1, where r is the nominal annual rate (as a decimal) and n is the number of compounding periods per year. For example, 5% compounded daily: (1 + 0.05/365)³⁶⁵ − 1 ≈ 5.13% APY. This calculator does it for any rate and frequency.
Only a little at normal rates. On a 5% account, daily compounding gives about 5.13% APY versus 5.00% with annual compounding — roughly $13 extra per year on $10,000. The effect grows at higher rates, but for most savers the headline APY matters far more than the compounding frequency.

Related Calculators

✔ Written & reviewed by Dr Sam — 20+ yrs in management & research leadership📅 Last updated June 2026📑 How we build & check these