What is the difference between APR and APY?

APR (Annual Percentage Rate) is the nominal rate quoted, ignoring compounding within the year. APY (Annual Percentage Yield) is the effective rate after compounding is applied. APY is always greater than APR whenever compounding happens more than once per year.

How is APY calculated from APR?

APY = (1 + APR/n)^n − 1, where n is the number of compounding periods per year. So 5% APR compounded monthly (n=12) gives an APY of 5.116%.

Which rate should I compare?

Always compare APYs (or effective rates) — they put accounts and loans on a fair like-for-like basis regardless of how often each one compounds.

Why is continuous compounding the upper limit?

As compounding frequency increases without bound, APY tends to e^(APR) − 1, where e is Euler's number. This is the theoretical maximum yield for a given APR.

📈 APY / APR Calculator

Convert between nominal annual rate (APR) and effective annual yield (APY) at any compounding frequency.

Nominal rate (APR, %)

Compounding frequency

ℹ️ Tip. When comparing savings accounts, look at APY. When comparing loans, look at APR (it includes mandatory fees by US regulation).

About the APY / APR Calculator

The APY / APR Calculator turns a nominal annual rate (APR) into an effective annual yield (APY) at any compounding frequency, and back again. This lets you compare savings accounts, CDs/bonds and loans on a fair like-for-like basis.

The formula

APY = (1 + APR / n)ⁿ − 1

where n is the number of compounding periods per year. For continuous compounding the formula reduces to APY = e^APR − 1.

Worked examples

5% APR compounded monthly → APY ≈ 5.116%
5% APR compounded daily → APY ≈ 5.127%
5% APR compounded continuously → APY ≈ 5.127% (same to 3 d.p.)
5% APR compounded annually → APY = 5.000% (no compounding effect within the year)

When does APR differ from APY?

For loans (mortgages, credit cards), US regulation requires APR to include certain mandatory fees, so APR is typically higher than the underlying interest rate. For savings accounts, APY captures the gain from intra-year compounding, so APY is typically higher than the quoted APR. Always compare like-with-like.

Frequently Asked Questions

Is APY always larger than APR? Yes — strictly larger whenever there is more than one compounding period per year. They are equal only for once-a-year compounding.

Which is "better" for savings? A higher APY means more interest earned, all else being equal.

Which is "better" for borrowing? A lower APR (or APY) means lower borrowing cost.

Why does continuous compounding give a clean answer? The limit of (1 + r/n)ⁿ as n → ∞ is e^r. This is one of the most important results in compound-interest theory.

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Important Note: This tool provides estimates and is not a substitute for professional financial advice. Always read the lender's or bank's full terms and conditions.

Related Calculators

Compound Interest — See how savings grow with daily/monthly compounding.
Savings Goal — Monthly savings needed to hit your target.
Loan Repayment — Monthly payments and total interest for any loan.