Short answer: APY is what you actually earn after compounding; APR is the plain rate before it. This converter works both directions. Example: a 4.4% APR compounded monthly is an APY of 4.490% — on $10,000 that’s $449 of interest in a year, not $440.
| Earnings in one year on your balance | — |
| Difference vs the stated rate | — |
See the full breakdown
Educational only — not financial advice. APY = (1 + APR/n)^n − 1 for n compoundings per year, and e^APR − 1 for continuous compounding; the reverse conversions are the exact algebraic inverses. US banks must disclose APY on deposit products (Regulation DD), which is why the APY on an account is the number you can trust for comparisons.
How this calculator works
APY = (1 + APR ÷ n)^n − 1, where n is how often interest compounds per year; for continuous compounding, APY = e^APR − 1. The reverse direction (APY → APR) uses the exact inverse formulas, and for continuous compounding the natural log: APR = ln(1 + APY). The breakdown table shows every standard frequency at once, which makes the pattern obvious: more frequent compounding helps, but with sharply diminishing returns — daily and monthly are nearly identical.
Worked example (APR 4.4%)
- Monthly compounding → APY 4.490%; daily → 4.498%; continuous → 4.498%; quarterly → 4.473%; annually → 4.400% (no compounding, so APY = APR).
- Reverse check: 5.00% APY, monthly compounding → APR 4.889%; continuous → 4.879%.
FAQs
Why do savings accounts quote APY but loans quote APR? Because each side quotes the number that flatters it: APY (with compounding) makes savings look bigger; APR on loans actually serves borrowers by including fees. US law (Regulation DD) requires APY disclosure on deposits. Does daily compounding beat monthly by much? Barely — at 4.4%, daily beats monthly by about 0.008 percentage points. Chase the rate, not the frequency. Is APY guaranteed? The APY on a savings account is variable and can change at any time; on a CD it’s fixed for the term. The conversion math is exact either way.
Sources: CFPB Regulation DD, Appendix A (APY formula), CFPB Regulation DD (Truth in Savings) Figures last verified Report a wrong number