APR vs APY
Same underlying rate, two conventions. APY counts compounding and APR does not — which is why you are quoted one on what you owe and the other on what you save.
APR to APY converter
Enter a rate and the compounding frequency to see its equivalent under the other convention.
- Treating it as an APR, the APY is
- 22.12%
- Treating it as an APY, the APR is
- 18.23%
One counts compounding, the other doesn’t
APR annualizes a periodic rate by simple multiplication. A monthly rate of 0.5% becomes an APR of 6%.
APY annualizes the same rate while accounting for compounding. That same 0.5% per month, compounded twelve times, becomes an APY of 6.168%.
Nothing about the underlying loan or deposit changed. Only the convention for describing it did.
APY = (1 + APR / n)^n − 1
where n is the number of compounding periods per year. The more frequent the
compounding, the wider the gap.
Why each side uses the one it does
This is not an accident of history — it is two different statutes, each requiring the convention that is honest for its product.
Lending discloses APR, under the Truth in Lending Act (Regulation Z). For credit, the APR’s job is to capture fees, which it does and APY does not.
Deposits disclose APY, under the Truth in Savings Act (Regulation DD). For savings, compounding is the entire benefit, so the disclosed number includes it.
The practical consequence is a systematic asymmetry: the rate you are quoted on what you owe understates the effective cost, and the rate you are quoted on what you save is stated at its effective value. Neither is deceptive on its own. The mismatch appears when you compare across them.
Where it actually bites
Credit cards. Card interest compounds daily. A 24% APR carried for a year costs about 27.1% — three points that never appear in any disclosure, because Regulation Z requires the APR.
Savings comparisons. A bank advertising a 4.9% “interest rate” compounded monthly and one advertising a 5.0% APY are effectively identical. If both quote APY, they are directly comparable, which is the point of Regulation DD.
Loan against deposit. Comparing a 6% mortgage APR against a 5% CD APY does not tell you the spread. Convert to a common basis first.
The rule of thumb
Comparing two loans? Both quote APR — compare directly. Two deposits? Both quote APY — compare directly. Comparing a loan against a deposit, or reasoning about what a card balance really costs you over a year? Convert.
Note also that for a loan with fees, converting the APR to an APY does not give you the true effective cost, because the APY formula assumes the APR is a pure interest rate. Fees are already folded into the APR in a way that the compounding formula was never designed to unwind. Treat the converter above as what it is: a compounding conversion, not a cost calculation.