APY vs. APR Calculator
Convert a nominal annual rate (APR) to its true effective yield (APY) at any compounding frequency — or do the reverse. See the gap in basis points and, if you want, the dollar difference on a real deposit.
APY vs. APR Calculator
Convert between the nominal rate (APR) and the effective rate (APY) at any compounding frequency, in either direction.
The stated annual rate, before compounding.
Used to show actual dollar earnings. Leave at $0 to hide.
APR (entered)
5.000%
Equivalent APY
5.116%
APY at monthly compounding
APY − APR Gap
0.116%
APR 5.000% ↔ APY 5.116%
Dollar earnings on $10,000.00 over 1 year
Using the same 5.000% APR, compounded at each frequency.
| Frequency | APY | End Balance | Interest Earned |
|---|---|---|---|
| Daily | 5.127% | $10,512.67 | $512.67 |
| Monthly(selected) | 5.116% | $10,511.62 | $511.62 |
| Quarterly | 5.095% | $10,509.45 | $509.45 |
| Annually | 5.000% | $10,500.00 | $500.00 |
APR vs. APY — the short version
APR (Annual Percentage Rate) is the nominalannual rate. It's the headline rate the bank quotes, before any compounding is applied. Think of it as the per-period rate multiplied by the number of periods — straight arithmetic, no growth-on-growth.
APY (Annual Percentage Yield) is the effectiveannual rate. It folds compounding into the number, so a 5% APR compounded monthly shows up as a 5.116% APY. APY is what you actually earn (on savings) or what you actually pay (on a loan that's being quoted in APY terms, which is rare in the US).
The two numbers are identical only when compounding happens exactly once per year. Every other frequency widens the gap a little — daily compounding produces the biggest spread, annual produces none.
The formulas
APR → APY
APY = (1 + APR / n)n − 1
Where n is the number of compounding periods per year (1 = annually, 4 = quarterly, 12 = monthly, 365 = daily).
APY → APR
APR = n × ((1 + APY)1/n − 1)
The inverse — if a bank quotes an APY and you want to know the underlying nominal rate.
Why banks quote APY on savings but APR on loans
It's a marketing asymmetry, locked in by regulation.
- On savings accounts and CDs, the bank pays you. The bigger the headline number, the more attractive the product looks — so they quote the larger APY. Truth in Savings Act (Reg DD) actually requires it: deposit accounts must disclose APY.
- On credit cards and personal loans, you pay the bank. The smaller the headline number, the friendlier the offer looks — so they quote APR. Truth in Lending Act (Reg Z) mandates this side too: consumer credit must be disclosed in APR.
The unfortunate result is that comparing “5% on my savings” to “5% on my loan” isn't apples-to-apples. If both compound monthly, the savings APY of 5% is a 4.89% APR, and the loan APR of 5% is a 5.12% APY. Always convert to the same metric before comparing.
The compounding-frequency effect, in one table
Same 5% nominal annual rate. The only thing that changes is how often interest gets added back to the balance.
| Frequency | Periods / Year | Effective APY | $10,000 after 1 yr |
|---|---|---|---|
| Annually | 1 | 5.000% | $10,500.00 |
| Quarterly | 4 | 5.095% | $10,509.45 |
| Monthly | 12 | 5.116% | $10,511.62 |
| Daily | 365 | 5.127% | $10,512.67 |
The full annual-to-daily spread is about 13 basis points on a 5% rate — roughly $13 per year per $10,000. Real, but rarely the difference that should decide where you park money.
Common gotchas APR and APY don't capture
- Promo and intro rates. A 6.00% APY for the first 3 months, then 0.40% after. A 0% intro APR for 18 months, then 24.99%. Neither headline number tells you the blended rate over your actual holding period — you have to do the math yourself.
- Fees that sit outside the APR. Credit card APR generally excludes annual fees, foreign transaction fees, and cash-advance fees. Personal loan APR sometimes excludes origination fees. Mortgage APR does include certain closing costs, which is why mortgage APRs run noticeably above their note rates.
- Balance and condition caps. Many high-APY accounts only pay the headline rate on the first $5,000–$25,000 of balance, or require direct deposits / minimum debit-card swipes each month. The APY shown is the maximum, not the guaranteed.
- Variable vs. fixed. APR on a credit card or HYSA APY is almost always variable — it moves with the prime rate or Fed funds rate. A CD APY is fixed for the term. The same headline number means very different things depending on which.
- Tax treatment. Interest earned in a taxable account is taxed as ordinary income. A 5% APY HYSA in a 24% bracket is really 3.8% after taxes. A 5% APY in a Roth IRA stays 5%. APY ignores this entirely.
A worked example, both directions
APR → APY.A credit card's purchase APR is 22.99%, compounded daily. The effective APY is (1 + 0.2299 / 365)365 − 1 ≈ 25.84%. Carrying a $5,000 balance for a year doesn't cost $1,150 — it costs about $1,292 once daily compounding does its work.
APY → APR. A HYSA advertises 4.50% APY, compounded daily. The underlying APR is 365 × ((1.045)1/365 − 1) ≈ 4.402%. That's the per-day rate × 365 that the bank is actually applying — the extra ~10 bps is the compounding effect.
Related Tools & Articles
Daily vs. Monthly vs. Annual Compounding
How much extra interest each frequency actually adds, over one year and over thirty
Compound Interest Calculator
Model any rate, term, and contribution schedule with a year-by-year chart
CD vs. Savings Account Calculator
Compare a fixed CD APY against a floating HYSA APY dollar-for-dollar
Compound Interest Formula
The full step-by-step walkthrough behind APY math
Frequently Asked Questions
What's the difference between APR and APY?
APR (Annual Percentage Rate) is the nominal rate, ignoring compounding. APY (Annual Percentage Yield) is the effective rate, after compounding is applied. A 5% APR compounded monthly is a 5.116% APY — the same underlying rate, but the APY is what you actually earn or pay in a year.
Why do banks quote APY on savings but APR on loans?
It's the number that makes their product look better. On a savings account, the bank pays you, so the higher APY number is the more attractive headline. On a loan, the bank charges you, so the lower APR number is the friendlier-looking quote. Federal Reg DD requires APY on deposit accounts, and Reg Z requires APR on loans — so the law actually mandates this asymmetry.
Does compounding frequency really matter that much?
Less than people think. At a 5% APR, the APY ranges from exactly 5.000% (annual compounding) to 5.127% (daily) — a spread of 13 basis points. That's about $13 per year on a $10,000 deposit. Bigger rates and longer time horizons widen the gap, but it never rivals the impact of the rate itself or how long the money stays invested.
If I see a 5% APR and a 5% APY, which is the better deal?
On a savings account, 5% APY is the better deal — that's what you actually earn. On a loan, 5% APR with no fees is the better deal because it's what you actually pay. The trap is comparing them directly: a 5% APR compounded daily is really a 5.127% APY, so 'APR vs. APY' is rarely an apples-to-apples comparison.
Does APR include fees on a loan?
Sort of — and that's the gotcha. Mortgage APR is required to include certain closing costs, so a mortgage APR is usually a bit higher than the note rate. Credit card APR generally does not include annual fees or transaction fees. Personal loan APR sometimes folds in origination fees, sometimes not. Always read the disclosure to know which fees are inside the APR and which are bolted on top.
How do I convert APY back to APR?
Use the formula APR = n × ((1 + APY)^(1/n) − 1), where n is the number of compounding periods per year. A 5.116% APY at monthly compounding (n = 12) converts to a 5.000% APR. The calculator above does this both directions automatically — flip the APR → APY toggle to APY → APR.
What about promo rates and introductory APRs?
Neither APR nor APY captures the time dimension of a promo. A 0% intro APR for 18 months on a credit card looks great, but the regular APR kicks in afterward. A 5.50% APY savings promo may only apply to balances under $25,000, or only for the first 3 months. Always check the term length and any balance/condition caps — the headline rate is only the rate while the promo lasts.