What's the difference between APR and APY?

APR (Annual Percentage Rate) is the nominal rate without considering intra-year compounding — what the bank quotes on a loan or what's printed on a credit card statement. APY (Annual Percentage Yield) factors in compounding — it's the actual yield you earn over a year, including interest on interest. For savings, APY > APR (slightly higher with more frequent compounding); for loans, the same is true in reverse.

What's the formula for converting APR to APY?

APY = (1 + APR/n)^n − 1, where n is the number of compounding periods per year. At 5% APR with daily compounding (n=365), APY = (1 + 0.05/365)^365 − 1 ≈ 5.127%. The gap (APY − APR) widens with more frequent compounding and higher rates.

Why does the bank advertise APY but my credit card shows APR?

US Regulation DD (Truth in Savings Act, 1991) requires deposit accounts to disclose APY so consumers can compare yields apples-to-apples. Regulation Z (Truth in Lending Act, 1968) requires loans + credit cards to disclose APR. The two regimes don't talk to each other — that's why you see APY on a savings ad and APR on a credit-card statement, even though they're computing the same underlying math.

What does 'continuous compounding' actually mean?

Continuous compounding is the mathematical limit of compounding frequency — what happens as n → infinity. The formula collapses to APY = e^APR − 1 (where e ≈ 2.71828). At 5% APR continuous, APY = 5.127% — almost identical to daily compounding because daily is already very close to the continuous ceiling. Banks don't compound continuously; it's a theoretical reference.

How much does compounding frequency actually matter?

Less than people think for typical savings rates. At 5% APR: annual compounding = 5.000% APY, monthly = 5.116% APY, daily = 5.127% APY, continuous = 5.127% APY. The jump from monthly to daily is only 1.1 basis points — meaningful on $1M+, almost invisible on $5K. Rate (APR) matters far more than compounding frequency.

If two banks quote different APYs, which wins?

Compare APYs directly — that's exactly why Regulation DD standardized the disclosure. A 4.90% APY beats a 5.00% APR with annual compounding (which is also 5.00% APY). If both quote APY, the higher number wins for a saver. Don't compare a 'rate' to an 'APY' without checking which is which.

What's the highest APY available in 2026?

Top US high-yield savings accounts are paying 4.5–5.25% APY (Capital One 360, Ally, Marcus, Bask Bank, etc.). Treasury Direct I-bonds and short-term T-bills can pay similar or slightly higher. Credit-union shared-CDs sometimes hit 5.5%+ with 12-month commitments. Anything advertised above 6% in this rate environment is either promotional (capped balance) or a risk-bearing product (not FDIC-insured).

Does my $1,000 actually earn the APY in the first year?

Yes — that's the entire point of APY. The 'effective annual yield' is the actual dollar interest credited over one year if the rate holds. On $1,000 at 5.127% APY (5.00% APR daily), you'll earn $51.27 in 12 months. If the rate changes mid-year (variable accounts), you'll earn the weighted blend.

Yes — interest income is reported on IRS Form 1099-INT and taxed as ordinary income at your federal + state rates. The displayed APY is gross of tax. To see your after-tax yield, multiply APY × (1 − your marginal tax rate). At 5.127% APY and a 24% federal bracket (no state tax), after-tax yield is 3.90%.

What's the difference between APY and total return on an investment?

APY is a stated rate for fixed-yield products (savings, CDs, money-market). Total return measures actual realized performance on a variable-yield investment (stocks, mutual funds, ETFs) — it's backward-looking and combines price change + dividends. Don't compare a 5.127% APY savings to a stated 'expected 10% stock market return' as equivalent — the latter is risk-bearing and the realized number varies.

What is APY for credit cards or loans?

Most credit cards and consumer loans don't quote APY — they quote APR. If they did, it would be the effective annual cost of the debt (slightly higher than APR for compounding products like cards). Mortgages legally quote APR (which already factors in some fees) but the underlying cost is approximately monthly-compound APR; the actual APY of a typical mortgage is fractionally higher.

Why is the continuous-compound rate the mathematical ceiling?

Because no matter how many times you compound, you can never exceed the limit defined by the constant e. Daily compounding (n=365) reaches 99.6% of the continuous limit; second-by-second (n=31.5M) reaches 99.999%. After daily, you're chasing fractions of basis points — banks don't bother going faster than daily because the marginal yield is below the operational cost.

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APY Calculator — APR ↔ APY Conversion + Earnings on $1,000

Convert between APR (nominal) and APY (effective) at any compounding frequency — annual, quarterly, monthly, weekly, or daily. See the spread, the continuous-compound ceiling, and the dollar earnings on $1,000 for one year and over 10 years.

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Reviewed by CalcBold Editorial · Sources: Federal Reserve Regulation DD (Truth in Savings Act) + FDIC published APY methodologyLast verified May 15, 2026Methodology

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Frequently Asked Questions

The most common questions we get about this calculator — each answer is kept under 60 words so you can scan.

What's the difference between APR and APY?
APR (Annual Percentage Rate) is the nominal rate without considering intra-year compounding — what the bank quotes on a loan or what's printed on a credit card statement. APY (Annual Percentage Yield) factors in compounding — it's the actual yield you earn over a year, including interest on interest. For savings, APY > APR (slightly higher with more frequent compounding); for loans, the same is true in reverse.
What's the formula for converting APR to APY?
APY = (1 + APR/n)^n − 1, where n is the number of compounding periods per year. At 5% APR with daily compounding (n=365), APY = (1 + 0.05/365)^365 − 1 ≈ 5.127%. The gap (APY − APR) widens with more frequent compounding and higher rates.
Why does the bank advertise APY but my credit card shows APR?
US Regulation DD (Truth in Savings Act, 1991) requires deposit accounts to disclose APY so consumers can compare yields apples-to-apples. Regulation Z (Truth in Lending Act, 1968) requires loans + credit cards to disclose APR. The two regimes don't talk to each other — that's why you see APY on a savings ad and APR on a credit-card statement, even though they're computing the same underlying math.
What does 'continuous compounding' actually mean?
Continuous compounding is the mathematical limit of compounding frequency — what happens as n → infinity. The formula collapses to APY = e^APR − 1 (where e ≈ 2.71828). At 5% APR continuous, APY = 5.127% — almost identical to daily compounding because daily is already very close to the continuous ceiling. Banks don't compound continuously; it's a theoretical reference.
How much does compounding frequency actually matter?
Less than people think for typical savings rates. At 5% APR: annual compounding = 5.000% APY, monthly = 5.116% APY, daily = 5.127% APY, continuous = 5.127% APY. The jump from monthly to daily is only 1.1 basis points — meaningful on $1M+, almost invisible on $5K. Rate (APR) matters far more than compounding frequency.
If two banks quote different APYs, which wins?
Compare APYs directly — that's exactly why Regulation DD standardized the disclosure. A 4.90% APY beats a 5.00% APR with annual compounding (which is also 5.00% APY). If both quote APY, the higher number wins for a saver. Don't compare a 'rate' to an 'APY' without checking which is which.
What's the highest APY available in 2026?
Top US high-yield savings accounts are paying 4.5–5.25% APY (Capital One 360, Ally, Marcus, Bask Bank, etc.). Treasury Direct I-bonds and short-term T-bills can pay similar or slightly higher. Credit-union shared-CDs sometimes hit 5.5%+ with 12-month commitments. Anything advertised above 6% in this rate environment is either promotional (capped balance) or a risk-bearing product (not FDIC-insured).
Does my $1,000 actually earn the APY in the first year?
Yes — that's the entire point of APY. The 'effective annual yield' is the actual dollar interest credited over one year if the rate holds. On $1,000 at 5.127% APY (5.00% APR daily), you'll earn $51.27 in 12 months. If the rate changes mid-year (variable accounts), you'll earn the weighted blend.
Is APY taxable?
Yes — interest income is reported on IRS Form 1099-INT and taxed as ordinary income at your federal + state rates. The displayed APY is gross of tax. To see your after-tax yield, multiply APY × (1 − your marginal tax rate). At 5.127% APY and a 24% federal bracket (no state tax), after-tax yield is 3.90%.
What's the difference between APY and total return on an investment?
APY is a stated rate for fixed-yield products (savings, CDs, money-market). Total return measures actual realized performance on a variable-yield investment (stocks, mutual funds, ETFs) — it's backward-looking and combines price change + dividends. Don't compare a 5.127% APY savings to a stated 'expected 10% stock market return' as equivalent — the latter is risk-bearing and the realized number varies.
What is APY for credit cards or loans?
Most credit cards and consumer loans don't quote APY — they quote APR. If they did, it would be the effective annual cost of the debt (slightly higher than APR for compounding products like cards). Mortgages legally quote APR (which already factors in some fees) but the underlying cost is approximately monthly-compound APR; the actual APY of a typical mortgage is fractionally higher.
Why is the continuous-compound rate the mathematical ceiling?
Because no matter how many times you compound, you can never exceed the limit defined by the constant e. Daily compounding (n=365) reaches 99.6% of the continuous limit; second-by-second (n=31.5M) reaches 99.999%. After daily, you're chasing fractions of basis points — banks don't bother going faster than daily because the marginal yield is below the operational cost.

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