APR to APY Converter
Convert between APR (annual percentage rate) and APY (annual percentage yield). Critical for comparing loans and savings accounts.
What this calculates
APR and APY measure the same thing — annual cost or return — but they account for compounding differently. APR is the simple annual rate (sum of periodic rates). APY is the effective rate after compounding. Banks legally must show both, but advertise whichever sounds better: APY on savings, APR on loans.
Formula & how it works
APY = (1 + APR / n)^n − 1, where n is compounding periods per year. APR = ((1 + APY)^(1/n) − 1) × n. Common n values: monthly = 12, daily = 365, continuous → APY = e^APR − 1.
Worked example
5 % APR compounded monthly: APY = (1 + 0.05/12)^12 − 1 = 0.05116 = 5.12 % APY. The difference (12 basis points) sounds small but on a $100K balance is $120 per year. Compounded daily: 5.13 % APY — minor extra gain.
Frequently asked questions
Which rate is shown on credit cards?
APR. Even though credit cards compound daily, regulation requires APR display. The effective rate (APY) is slightly higher — about 0.2–0.3 points higher than APR for typical card rates.
Which rate matters more?
APY for true comparison, since it accounts for compounding. APR is fine when comparing within the same compounding frequency, but APY is universal.
Why don't savings banks show APR?
Because APY looks higher. The 5.00 % APY savings account has a lower APR (~4.88 %). The bank is required to show APY by Truth in Savings Act in the US.
What's the difference at high rates?
It grows non-linearly. At 24 % APR (typical credit card) compounded daily, APY is ~27.1 % — a 3-point gap. At 1 % APR, the gap is invisible.
Related calculators
- Compound InterestSee how money grows over time with compounding. Enter principal, rate, time, and optional monthly contributions to project future value.
- Credit Card PayoffSee how long it takes to pay off a credit card balance and how much interest you'll pay. Compare minimum payments versus a fixed monthly amount.