APY Calculator
Convert a nominal APR into the APY you actually earn — or work backwards from an advertised APY to the underlying APR. Pick the compounding frequency and see the exact effect it has on your yield.
5.00% APR with monthly compounding equals
APY (effective yield)
5.116%
Continuous compounding limit
5.127%
5% APR at every compounding frequency
| Compounding | Periods / year | APY |
|---|---|---|
| Daily | 365 | 5.127% |
| Monthly | 12 | 5.116% |
| Quarterly | 4 | 5.095% |
| Annually | 1 | 5.00% |
| Continuous (limit) | ∞ | 5.127% |
The APY formula
APY = (1 + r/n)n − 1
where r is the APR as a decimal and n is the number of compounding periods per year (365 daily, 12 monthly, 4 quarterly, 1 annually).
Worked example: 5% APR compounded monthly is (1 + 0.05/12)12 − 1 = 0.05116 = 5.12% APY. The reverse direction solves for r: APR = n × ((1 + APY)1/n − 1).
As n grows, APY approaches the continuous compounding limit er − 1. At 5% APR that is e0.05 − 1 = 5.127% — only 0.001 percentage points above daily compounding, which is why banks stopping at daily costs you essentially nothing.
Why banks quote APY for savings but APR for loans
APY is always the bigger number, so deposit products are advertised with it; APR is the smaller number, so loans are advertised with that. Both are legally mandated in the US (Truth in Savings for deposits, Truth in Lending for credit), which conveniently matches what looks best in each ad. When you compare products, put them on the same basis first. To see what a given APY does to real dollars over time, try the compound interest calculator, check locked-term earnings with the CD calculator, or plan monthly contributions with the savings calculator.