Comprehensive Guide
Learn more in our Personal Finance Guide.
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.