How it works
APR to APY conversion translates a nominal annual rate into the effective annual yield that compounding actually produces — the two diverge whenever interest compounds more than once per year. APR states the rate flat: 12% means 12% regardless of timing. APY compounds: 12% compounded monthly becomes (1 + 0.12/12)^12 − 1, or 12.682%. The gap grows with both the rate and the frequency — at 5% nominal, daily compounding yields 5.13%, a rounding-error difference; at 20% credit-card territory, daily compounding turns a 20% APR into nearly 21.94% APY, which is why carried balances grow faster than the headline suggests. Financial institutions exploit the asymmetry deliberately: savings accounts are advertised in APY because it looks bigger, loans in APR because it looks smaller. Converting puts both sides on the effective-yield footing, the only basis on which comparison is honest. This calculator works in either direction — nominal to effective and back — for any compounding frequency, then prices the difference in dollars: what $10,000 earns at each rate over a year. One caveat keeps loan comparisons fair: quoted loan APRs under Truth-in-Lending also fold fees into the figure, so compare loan offers APR-to-APR, never a raw rate against an APY.
Formula
APY = (1 + APR/m)^m − 1 | APR = m × ((1 + APY)^(1/m) − 1), where m = compounds per year
Tips
- Compare savings offers in APY and loans in APR — converted, never mixed raw.
- Compounding frequency matters more as rates rise: check daily versus monthly.
- Credit-card APR compounds daily — convert it to see what a balance truly costs.
- Loan APRs fold in fees under Truth-in-Lending; compare offers APR-to-APR only.
- At low rates the gap is pennies; at 20%+ it is hundreds a year per $10,000.
Frequently asked questions
- What is the difference between APR and APY?
- APR is the nominal annual rate with no compounding; APY is the effective rate including it. A 12% APR compounded monthly equals a 12.682% APY — same underlying rate, different accounting of time. Any comparison across the two without conversion is meaningless.
- How do I convert APR to APY?
- Divide the APR by the number of compounding periods, add one, raise to the power of the number of periods, and subtract one: APY = (1 + APR/m)^m − 1. For 12% APR compounded monthly, (1.01)^12 − 1 gives 12.682%. The calculator runs it instantly, including the reverse direction.
- Why is APY higher than APR?
- Because compounding pays interest on interest. Each period's earnings join the base before the next period accrues, so a year of frequent compounding produces slightly more than the flat rate times one. The effect scales with both the rate level and the number of compounding periods.
- Do banks advertise APR or APY?
- Strategically both: savings products use APY because compounding inflates it, loan products use APR because the un-compounded figure flatters borrowers. Neither is dishonest — regulation mandates the formats — but comparing a savings APY directly against a loan APR without converting misleads systematically.
- What is 5% APR compounded daily in APY?
- (1 + 0.05/365)^365 − 1 = 5.1267% APY. The gap of about 0.13 points looks trivial until multiplied: on $10,000 it is roughly $13 a year, and on a five-figure credit-card balance at 25% APR compounded daily, the equivalent gap approaches $60 annually.