FINANCIAL · APY TO APR
APY to APR Calculator
Convert between APY and APR for any compounding frequency. See the effective annual rate and the compounding premium for savings accounts, CDs, and loan comparisons.
APY (= EAR) is the true annual yield after compounding. APR is the nominal rate before compounding is applied. For loans, lender APR may include fees — this calculator converts rate-only (no fee component).
About This Calculator
Convert between APY (Annual Percentage Yield) and APR (Annual Percentage Rate) for any compounding frequency — daily, monthly, quarterly, semi-annually, or annually. See the effective annual rate (EAR) and the compounding premium that separates APY from the nominal APR.
How It Works
APY measures how much you actually earn (or pay) in a year after compounding. APR is the stated nominal rate before compounding is applied. The two diverge for all compounding frequencies except annual. Select the direction, enter the known rate, pick a compounding frequency, and the calculator instantly shows the converted rate and the spread (how much compounding adds to the effective yield). The effective annual rate (EAR) is always equal to APY — it's just another name for the same concept used in academic and banking contexts.
The Formula
APY = (1 + APR/n)^n − 1 APR = n × ((1 + APY)^(1/n) − 1)
- APY
- Annual Percentage Yield (effective annual rate)
- APR
- Annual Percentage Rate (nominal annual rate)
- n
- compounding periods per year (daily=365, monthly=12, etc.)
Frequently Asked Questions
- What is the difference between APY and APR?
- APR (Annual Percentage Rate) is the nominal annual interest rate before compounding — the number banks quote in marketing. APY (Annual Percentage Yield) is the actual return after all compounding is applied over a year. For any compounding frequency more than once per year, APY > APR. For annual compounding, APY = APR. When comparing savings accounts, use APY; it tells you exactly how much you'll earn in a year.
- Why does compounding frequency matter?
- The more often interest compounds, the higher the effective yield. An APR of 5% compounded daily produces APY ≈ 5.127%, while the same 5% APR compounded monthly gives APY ≈ 5.116%, and annually gives exactly 5.00%. The difference is called the compounding premium. For most consumer savings rates, the daily-vs-monthly gap is small, but it grows significantly at higher rates or longer time horizons.
- When should I use APR vs APY?
- Use APY to compare savings accounts, money market accounts, and CDs — it reflects exactly what you'll earn. Use APR when comparing loan products (mortgages, auto loans, personal loans) — though be aware that for loans, lenders may define APR to include fees beyond the interest rate, which this calculator does not handle. This calculator converts rate-only, with no fee component.
- What is the effective annual rate (EAR)?
- EAR is the same as APY — just a term more common in academic finance and some institutional contexts. It equals the actual annual return after compounding. EAR = (1 + APR/n)^n − 1, which is identical to the APY formula. You may see EAR, APY, and "effective interest rate" used interchangeably; they all mean the annualized rate after compounding.
- Does this calculator apply to loan APR?
- This calculator converts between the pure nominal APR and APY using the compounding formula only — no fees are included. For consumer loans (mortgages, auto, personal), regulatory APR (Reg Z / TILA) must include certain fees, making the disclosed APR higher than the pure rate. If a lender quotes you an APR that includes origination fees, the true cost is higher than what this calculator shows for the same APR. Always confirm whether a quoted APR is fee-inclusive or rate-only.