APR ↔ APY Calculator (Nominal vs Effective Annual Rate)
Enter a nominal annual rate (APR) and a compounding frequency to see the effective annual yield (APY) instantly — or solve the inverse. The calculator also shows the same APR at every common compounding cadence and the 10-year compound growth of $1,000, so you can compare credit-card, savings-account and mortgage rates on a single fair basis.
Enter a valid rate (−100% < rate ≤ 1000%).
Effective annual yield (APY)
—
$1,000 grown for 10 years
—
APY at every compounding frequency
| Frequency | n / yr | APY |
|---|
APR = nominal annual rate (no compounding); APY = effective annual yield (with compounding). To compare products, convert both to the same basis.
Formula
APY = (1 + APR/n) ^ n − 1 (n = compounding periods per year; APR and APY entered as decimals) Continuous (n → ∞): APY = e^APR − 1 Inverse: APR = n × ((1 + APY)^(1/n) − 1); continuous: APR = ln(1 + APY)
- · APR = nominal annual rate (a.k.a. annual percentage rate) — simply the per-period rate multiplied by the number of periods, with no compounding adjustment.
- · APY = effective annual yield (US) / effective annual rate (EAR / AER in UK and EU) — includes compounding, so it is always ≥ APR.
- · Higher compounding frequency raises APY; continuous compounding is the theoretical ceiling. An 8% APR compounded monthly gives APY ≈ 8.30%; continuously, APY ≈ 8.33%.
- · Source: US Truth in Lending Act (Regulation Z, APR disclosure) and Truth in Savings Act (Regulation DD, APY disclosure) — the definitions most global banks adopt.
- · When comparing products, always convert to the same basis. Credit cards quote APR; savings accounts and term deposits quote APY.
- · This tool assumes a flat rate for the whole year with no fees or taxes. Real annualised returns also need to account for transaction fees, withholding tax and prepayment terms.
Frequently asked
APR vs APY vs EAR vs AER — what is the difference?
APR (Annual Percentage Rate) is the nominal annual rate — the per-period rate × periods per year, with no compounding adjustment. APY (Annual Percentage Yield) is the US Regulation DD disclosure standard for savings accounts and includes compounding. EAR (Effective Annual Rate) and AER (Annual Equivalent Rate) are the UK and EU names for the same concept. So APY = EAR = AER. The same APR at different compounding frequencies produces different APYs — which is exactly what this calculator is for.
My bank advertises a "5% interest" term deposit — is that APR or APY, and how much will I actually receive?
Hong Kong banks (and US savings products under Reg DD) typically quote APY; UK/EU products usually quote AER. If a leaflet only says "5% interest", look in the fine print for the compounding cadence. A 5% APR compounded monthly gives APY ≈ 5.116%; if the 5% is already an APY, the equivalent monthly APR is ≈ 4.889%. The difference is small but real — punch the terms into this tool to see the apples-to-apples figure.
What is "continuous compounding" and does it matter in real life?
Continuous compounding is the n → ∞ limit — interest is credited at every instant, giving APY = e^APR − 1. In retail banking it is unused because the gap between daily compounding (n = 365) and continuous compounding is under 0.001 percentage points. It mostly shows up in academic work, derivatives pricing (e.g. the Black-Scholes option model) and actuarial discounting.
My credit card says "24% APR" — how much interest am I actually paying each month?
24% APR ÷ 12 = 2% per monthly billing period. Compounded for 12 months, APY = (1.02)^12 − 1 ≈ 26.82%. If you carry $100 of balance for a year, it grows to $126.82. If the card uses daily periodic rates (n = 365), the APY climbs to ≈ 27.11%. That gap of several percentage points between the advertised APR and what you actually pay is precisely why personal-finance writers urge "pay the balance in full each month".
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