APR vs APY: Two Rates, One Truth
The same account can honestly advertise two different numbers:
- APR (nominal rate) — the yearly rate before considering how often interest compounds within the year.
- APY (effective rate) — what you actually earn or pay across a year once intra-year compounding is included.
A 6% APR compounded monthly is really 6.17% APY; compounded daily, 6.18%. Banks predictably advertise APY on savings (bigger number) and APR on loans (smaller number). This converter strips the marketing and puts every offer on the same scale.
The Conversion Formulas
APR = n × [(1 + APY)1/n − 1]
where n = compounding periods per year (12 monthly, 365 daily, 4 quarterly…).
Effect of frequency on a 6% APR
| Compounding | n | APY |
|---|---|---|
| Annually | 1 | 6.000% |
| Quarterly | 4 | 6.136% |
| Monthly | 12 | 6.168% |
| Daily | 365 | 6.183% |
Frequency helps, with hard diminishing returns — daily vs monthly is worth just 0.015 points here. A better rate beats better frequency every time.
Worked Comparisons
Savings: which account wins?
| Offer | Advertised | APY (true yield) |
|---|---|---|
| Bank A | 5.90% APR, daily compounding | 6.077% |
| Bank B | 6.00% APR, annual compounding | 6.000% |
The "smaller" headline number wins. On $50,000 over 5 years, A ends ≈ $186 ahead.
Credit card reality check
A 24% APR card compounding daily has an effective annual rate of (1 + 0.24/365)365 − 1 ≈ 27.1% — the number that actually applies to carried balances.
When Each Number Matters
| Situation | Compare by | Why |
|---|---|---|
| Savings accounts / CDs | APY | Captures compounding you receive |
| Loans & credit cards | APR (with fees) → effective rate | US law mandates APR disclosure; effective rate shows carried-balance cost |
| Investments quoted monthly | Annualize: (1+m)12 − 1 | "1% per month" is 12.68%/yr, not 12% |
| Any two offers with different frequencies | Convert both to APY | Only equal-basis comparison is valid |
Practical Rules
- Never compare an APR to an APY directly — convert first; the gap grows with rate and frequency.
- "Per month" rates deserve special suspicion: small monthly numbers annualize to big ones (2%/mo ≈ 26.8%/yr).
- On loans, fold fees in: a "0-fee 7%" loan can beat a "6.5% + 2 points" loan — the disclosed APR helps, and the Payment Calculator can extract the true rate from real cash flows.
- For growth over multiple years, continue to the Compound Interest Calculator — APY is the yearly lens, compounding curves are the long view.
The Bottom Line
Interest rates only mean something on a common basis, and APY is that basis. One conversion above tells you whether the flashy savings offer beats the plain one, and what your card balance is really charging you. Two numbers, one truth — always compare on the effective side of it.